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Although the hardware is limited to four separate sound channels, software such as "OctaMED" uses software mixing to allow eight or more virtual channels, and it was possible for software to mix two hardware channels to achieve a single 14-bit resolution channel by playing with the volumes of the channels in such a way that one of the source channels contributes the most significant bits and the other the least.
The quality of the Amiga's sound output, and the fact that sound hardware is part of the standard chipset and easily addressed by software, were standout features of Amiga hardware unavailable on IBM PC compatibles for years. Third-party sound cards exist that provide DSP functions, multi-track direct-to-disk recording, multiple hardware sound channels and 16-bit and beyond resolutions. A retargetable sound API called AHI was developed allowing these cards to be used transparently by the OS and software.
Kickstart firmware.
Kickstart is the firmware upon which AmigaOS is bootstrapped. Its purpose is to initialize the Amiga hardware and core components of AmigaOS and then attempt to boot from a bootable volume, such as a floppy disk or hard disk drive. Most models (excluding the Amiga 1000) come equipped with Kickstart on an embedded ROM-chip.
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There are various editions of Kickstart ROMs starting with Kickstart v1.1 for the Amiga 1000, v1.2 and v1.3 for the A500, Kickstart v2.1 on A500+, Kickstart v2.2 for A600 and dual ROMs for Kickstart v3.0 and 3.1 for A1200 and A4000. After Commodore's demise there have been new Kickstart v3.1 ROMs made available for both the A500 and A600 Computers. Amiga Software is mostly backward compatible, but v2.1 ROMs and newer differ slightly, which can cause software glitches with earlier programs. To help address this and to get earlier programs to work with later Kickstart ROMs, some tools have been produced such as RELOKIK 1.4 and MAKE IT WORK! for the A600 and A1200. They revert the system to temporarily boot in Kickstart v1.3.
Keyboard and mouse.
The keyboard on Amiga computers is similar to that found on a mid-80s IBM PC: Ten function keys, a numeric keypad, and four separate directional arrow keys. Caps Lock and Control share space to the left of A. Absent are Home, End, Page Up, and Page Down keys: These functions are accomplished on Amigas by pressing shift and the appropriate arrow key. The Amiga keyboard adds a Help key, which a function key usually acts as on PCs (usually F1). In addition to the Control and Alt modifier keys, the Amiga has 2 "Amiga" keys, rendered as "Open Amiga" and "Closed Amiga" similar to the Open/Closed Apple logo keys on Apple II keyboards. The left is used to manipulate the operating system (moving screens and the like) and the right delivers commands to the application. The absence of Num lock frees space for more mathematical symbols around the numeric pad.
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Like IBM-compatible computers, the mouse has two buttons, but in AmigaOS, pressing and holding the right button replaces the system status line at the top of the screen with a Maclike menu bar. As with Apple's Mac OS prior to Mac OS 8, menu options are selected by releasing the button over that option, not by left clicking. Menu items that have a Boolean toggle state can be left clicked whilst the menu is kept open with the right button, which allows the user – for example – to set some selected text to bold, underline and italics in one visit to the menus.
The mouse plugs into one of two Atari joystick ports used for joysticks, game paddles, and graphics tablets. Although compatible with analog joysticks, Atari-style digital joysticks became standard. Unusually, two independent mice can be connected to the joystick ports; some games, such as Lemmings, were designed to take advantage of this.
Other peripherals and expansions.
The Amiga was one of the first computers for which inexpensive sound sampling and video digitization accessories were available. As a result of this and the Amiga's audio and video capabilities, the Amiga became a popular system for editing and producing both music and video.
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Many expansion boards were produced for Amiga computers to improve the performance and capability of the hardware, such as memory expansions, SCSI controllers, CPU boards, and graphics boards. Other upgrades include genlocks, network cards for Ethernet, modems, sound cards and samplers, video digitizers, extra serial ports, and IDE controllers. Additions after the demise of Commodore company are USB cards. The most popular upgrades were memory, SCSI controllers and CPU accelerator cards. These were sometimes combined into one device.
Early CPU accelerator cards used the full 32-bit CPUs of the 68000 family such as the Motorola 68020 and Motorola 68030, almost always with 32-bit memory and usually with FPUs and MMUs or the facility to add them. Later designs feature the Motorola 68040 or Motorola 68060. Both CPUs feature integrated FPUs and MMUs. Many CPU accelerator cards also had integrated SCSI controllers.
Phase5 designed the PowerUP boards (Blizzard PPC and CyberStorm PPC) featuring both a 68k (a 68040 or 68060) and a PowerPC (603 or 604) CPU, which are able to run the two CPUs at the same time and share the system memory. The PowerPC CPU on PowerUP boards is usually used as a coprocessor for heavy computations; a powerful CPU is needed to run MAME for example, but even decoding JPEG pictures and MP3 audio was considered heavy computation at the time. It is also possible to ignore the 68k CPU and run Linux on the PPC via project Linux APUS, but a PowerPC-native AmigaOS promised by Amiga Technologies GmbH was not available when the PowerUP boards first appeared.
24-bit graphics cards and video cards were also available. Graphics cards were designed primarily for 2D artwork production, workstation use, and later, gaming. Video cards are designed for inputting and outputting video signals, and processing and manipulating video.
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In the North American market, the "NewTek Video Toaster" was a video effects board that turned the Amiga into an affordable video processing computer that found its way into many professional video environments. One well-known use was to create the special effects in early series of "Babylon 5". Due to its NTSC-only design, it did not find a market in countries that used the PAL standard, such as in Europe. In those countries, the "OpalVision" card was popular, although less featured and supported than the Video Toaster. Low-cost time base correctors (TBC) specifically designed to work with the Toaster quickly came to market, most of which were designed as standard Amiga bus cards.
Various manufacturers started producing PCI busboards for the A1200, A3000 and A4000, allowing standard Amiga computers to use PCI cards such as graphics cards, Sound Blaster sound cards, 10/100 Ethernet cards, USB cards, and television tuner cards. Other manufacturers produced hybrid boards that contained an Intel x86 series chip, allowing the Amiga to emulate a PC.
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PowerPC upgrades with Wide SCSI controllers, PCI busboards with Ethernet, sound and 3D graphics cards, and tower cases allowed the A1200 and A4000 to survive well into the late nineties.
Expansion boards were made by Richmond Sound Design that allow their show control and sound design software to communicate with their custom hardware frames either by ribbon cable or fiber optic cable for long distances, allowing the Amiga to control up to eight million digitally controlled external audio, lighting, automation, relay and voltage control channels spread around a large theme park, for example. See Amiga software for more information on these applications.
Other devices included the following:
Serial ports.
The Commodore A2232 board provides seven RS-232C serial ports in addition to the Amiga's built-in serial port. Each port can be driven independently at speeds of 50 to . There is, however, a driver available on Aminet that allows two of the serial ports to be driven at . The serial card used the 65CE02 CPU clocked at . This CPU was also part of the CSG 4510 CPU core that was used in the Commodore 65 computer.
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Networking.
Amiga has three networking interface APIs:
Different network media were used:
Models and variants.
The original Amiga models were produced from 1985 to 1996. They are, in order of production: 1000, 2000, 500, 1500, 2500, 3000, 3000UX, 3000T, CDTV, 500+, 600, 4000, 1200, CD32, and 4000T. The PowerPC-based AmigaOne computers were later marketed beginning in 2002. Several companies and private persons have also released Amiga clones and still do so today.
Commodore Amiga.
The first Amiga model, the Amiga 1000, was launched in 1985. In 2006, PC World rated the Amiga 1000 as the seventh greatest PC of all time, stating "Years ahead of its time, the Amiga was the world's first multimedia, multitasking personal computer".
Commodore updated the desktop line of Amiga computers with the Amiga 2000 in 1987, the Amiga 3000 in 1990, and the Amiga 4000 in 1992, each offering improved capabilities and expansion options. The best-selling models were the budget models, however, particularly the highly successful Amiga 500 (1987) and the Amiga 1200 (1992). The Amiga 500+ (1991) was the shortest-lived model, replacing the Amiga 500 and lasting only six months until it was phased out and replaced with the Amiga 600 (1992). The A600 was only intended as a temporary gap filler until the A1200 was available for sale. The A600 was actually designed as a portable system, hence the lack of numeric Keypad, and it was originally to be named Amiga 300. Some early A600 models have retained the original A300 logo printed on the mainboard. The Amiga 600 was quickly replaced by the Amiga 1200.
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The CDTV, launched in 1991, was a CD-ROM-based game console, Computer and multimedia appliance based on the Amiga A500 with the same v1.3 Kickstart ROM, several years before CD-ROM drives were common. The cost of CDTV media production and the CD-ROM drives at the time discouraged potential buyers and the system never achieved any real success. The CDTV was however one of the first ever CD-ROM-based machines that were mass produced. A CDTV legacy is the external A570 CD-ROM drive expansion for the A500 computer.
Commodore's last Amiga offering before filing for bankruptcy was the Amiga CD32 (1993), a 32-bit CD-ROM games console produced until mid 1994. Although discontinued after Commodore's demise it met with moderate commercial success in Europe. The CD32 was a next-generation CDTV, and it was designed and released by Commodore before the Playstation. It was Commodore's last attempt to enter the ever growing video-game console market.
Following purchase of Commodore's assets by Escom in 1995, the A1200 and A4000T continued to be sold in small quantities until 1996, though the ground lost since the initial launch and the prohibitive expense of these units meant that the Amiga line never regained any real popularity.
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Several Amiga models contained references to songs by the rock band The B-52's. Early A500 units had the words "B52/ROCK LOBSTER" silk-screen printed onto their printed circuit board, a reference to the song "Rock Lobster" The Amiga 600 referenced "JUNE BUG" (after the song "Junebug") and the Amiga 1200 had "CHANNEL Z" (after "Channel Z"), and the CD-32 had "Spellbound."
AmigaOS 4 systems.
AmigaOS 4 is designed for PowerPC Amiga systems. It is mainly based on AmigaOS 3.1 source code, with some parts of version 3.9. Currently runs on both Amigas equipped with CyberstormPPC or BlizzardPPC accelerator boards, on the Teron series based AmigaOne computers built by Eyetech under license by Amiga, Inc., on the Pegasos II from Genesi/bPlan GmbH, on the ACube Systems Srl Sam440ep / Sam460ex / AmigaOne 500 systems and on the A-EON AmigaOne X1000.
AmigaOS 4.0 had been available only in developer pre-releases for numerous years until it was officially released in December 2006. Due to the nature of some provisions of the contract between Amiga Inc. and Hyperion Entertainment (the Belgian company that is developing the OS), the commercial AmigaOS 4 had been available only to licensed buyers of AmigaOne motherboards.
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AmigaOS 4.0 for Amigas equipped with PowerUP accelerator boards was released in November 2007. Version 4.1 was released in August 2008 for AmigaOne systems, and in May 2011 for Amigas equipped with PowerUP accelerator boards. The most recent release of AmigaOS for all supported platforms is 4.1 update 5. Starting with release 4.1 update 4 there is an Emulation drawer containing official AmigaOS 3.x ROMs (all classic Amiga models including CD32) and relative Workbench files.
Acube Systems entered an agreement with Hyperion under which it has ported AmigaOS 4 to its Sam440ep and Sam460ex line of PowerPC-based motherboards. In 2009 a version for Pegasos II was released in co-operation with Acube Systems. In 2012, A-EON Technology Ltd manufactured and released the AmigaOne X1000 to consumers through their partner, Amiga Kit who provided end-user support, assembly and worldwide distribution of the new system.
Amiga hardware clones.
Long-time Amiga developer MacroSystem entered the Amiga-clone market with their DraCo non-linear video editing system. It appears in two versions, initially a tower model and later a cube. DraCo expanded upon and combined a number of earlier expansion cards developed for Amiga (VLabMotion, Toccata, WarpEngine, RetinaIII) into a true Amiga-clone powered by the Motorola 68060 processor. The DraCo can run AmigaOS 3.1 up through AmigaOS 3.9. It is the only Amiga-based system to support FireWire for video I/O. DraCo also offers an Amiga-compatible Zorro-II expansion bus and introduced a faster custom DraCoBus, capable of transfer rates (faster than Commodore's Zorro-III). The technology was later used in the Casablanca system, a set-top-box also designed for non-linear video editing.
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In 1998, Index Information released the Access, an Amiga-clone similar to the Amiga 1200, but on a motherboard that could fit into a standard -inch drive bay. It features either a 68020 or 68030 CPU, with a AGA chipset, and runs AmigaOS 3.1.
In 1998, former Amiga employees (John Smith, Peter Kittel, Dave Haynie and Andy Finkel to mention few) formed a new company called PIOS. Their hardware platform, PIOS One, was aimed at Amiga, Atari and Macintosh users. The company was renamed to Met@box in 1999 until it folded.
The NatAmi (short for "Native Amiga") hardware project began in 2005 with the aim of designing and building an Amiga clone motherboard that is enhanced with modern features. The NatAmi motherboard is a standard Mini-ITX-compatible form factor computer motherboard, powered by a Motorola/Freescale 68060 and its chipset. It is compatible with the original Amiga chipset, which has been inscribed on a programmable FPGA Altera chip on the board. The NatAmi is the second Amiga clone project after the Minimig motherboard, and its history is very similar to that of the C-One mainboard developed by Jeri Ellsworth and Jens Schönfeld.
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The NatAmi is the second Amiga clone project after the Minimig motherboard, and its history is very similar to that of the C-One mainboard developed by Jeri Ellsworth and Jens Schönfeld. From a commercial point of view, Natami's circuitry and design are currently closed source. One goal of the NatAmi project is to design an Amiga-compatible motherboard that includes up-to-date features but that does not rely on emulation (as in WinUAE), modern PC Intel components, or a modern PowerPC mainboard. As such, NatAmi is not intended to become another evolutionary heir to classic Amigas, such as with AmigaOne or Pegasos computers. This "purist" philosophy essentially limits the resulting processor speed but puts the focus on bandwidth and low latencies. The developers also recreated the entire Amiga chipset, freeing it from legacy Amiga limitations such as two megabytes of audio and video graphics RAM as in the AGA chipset, and rebuilt this new chipset by programming a modern FPGA Altera Cyclone IV chip. Later, the developers decided to create from scratch a new software-form processor chip, codenamed "N68050" that resides in the physical Altera FPGA programmable chip.
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In 2006, two new Amiga clones were announced, both using FPGA-based hardware synthesis to replace the Amiga OCS custom chipset. The first, the Minimig, is a personal project of Dutch engineer Dennis van Weeren. Referred to as "new Amiga hardware", the original model was built on a Xilinx Spartan-3 development board, but soon a dedicated board was developed. The minimig uses the FPGA to reproduce the custom Denise, Agnus, Paula and Gary chips as well as both 8520 CIAs and implements a simple version of Amber. The rest of the chips are an actual 68000 CPU, ram chips, and a PIC microcontroller for BIOS control. The design for Minimig was released as open-source on July 25, 2007. In February 2008, an Italian company Acube Systems began selling Minimig boards. A third party upgrade replaces the PIC microcontroller with a more powerful ARM processor, providing more functionality such as write access and support for hard disk images. The Minimig core has been ported to the FPGArcade "Replay" board. The Replay uses an FPGA with about three times more capacity and that does support the AGA chipset and a 68020 soft core with 68030 capabilities. The Replay board is designed to implement many older computers and classic arcade machines.
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The second is the Clone-A system announced by Individual Computers. As of mid-2007 it has been shown in its development form, with FPGA-based boards replacing the Amiga chipset and mounted on an Amiga 500 motherboard.
Operating systems.
AmigaOS.
AmigaOS is a single-user multitasking operating system. It was one of the first commercially available consumer operating systems for personal computers to implement preemptive multitasking. It was developed first by Commodore International and initially introduced in 1985 with the Amiga 1000. John C. Dvorak wrote in "PC Magazine" in 1996:
AmigaOS combines a command-line interface and graphical user interface. AmigaDOS is the disk operating system and command line portion of the OS and Workbench the native graphical windowing, graphical environment for file management and launching applications. AmigaDOS allows long filenames (up to 107 characters) with whitespace and does not require filename extensions. The windowing system and user interface engine that handles all input events is called Intuition.
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The multi-tasking kernel is called Exec. It acts as a scheduler for tasks running on the system, providing pre-emptive multitasking with prioritised round-robin scheduling. It enabled true pre-emptive multitasking in as little as 256 KB of free memory.
AmigaOS does not implement memory protection; the 68000 CPU does not include a memory management unit. Although this speeds and eases inter-process communication because programs can communicate by simply passing a pointer back and forth, the lack of memory protection made the AmigaOS more vulnerable to crashes from badly behaving programs than other multitasking systems that did implement memory protection, and Amiga OS is fundamentally incapable of enforcing any form of security model since any program had full access to the system. A co-operational memory protection feature was implemented in AmigaOS 4 and could be retrofitted to old AmigaOS systems using Enforcer or CyberGuard tools.
The problem was somewhat exacerbated by Commodore's initial decision to release documentation relating not only to the OS's underlying software routines, but also to the hardware itself, enabling intrepid programmers who had developed their skills on the Commodore 64 to POKE the hardware directly, as was done on the older platform. While the decision to release the documentation was a popular one and allowed the creation of fast, sophisticated sound and graphics routines in games and demos, it also contributed to system instabilityas some programmers lacked the expertise to program at this level. For this reason, when the new AGA chipset was released, Commodore declined to release low-level documentation in an attempt to force developers into using the approved software routines.
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The latest version for the PPC Amigas is the AmigaOS 4.1 and for the 68k Amigas is the AmigaOS 3.2.2
Influence on other operating systems.
AmigaOS directly or indirectly inspired the development of various operating systems. MorphOS and AROS clearly inherit heavily from the structure of AmigaOS as explained directly in articles regarding these two operating systems. AmigaOS also influenced BeOS, which featured a centralized system of Datatypes, similar to that present in AmigaOS. Likewise, DragonFly BSD was also inspired by AmigaOS as stated by Dragonfly developer Matthew Dillon who is a former Amiga developer. WindowLab and amiwm are among several window managers for the X Window System seek to mimic the Workbench interface. IBM licensed the Amiga GUI from Commodore in exchange for the REXX language license. This allowed OS/2 to have the WPS (Workplace Shell) GUI shell for OS/2 2.0, a 32-bit operating system.
Unix and Unix-like systems.
Commodore-Amiga produced Amiga Unix, informally known as Amix, based on AT&T SVR4. It supports the Amiga 2500 and Amiga 3000 and is included with the Amiga 3000UX. Among other unusual features of Amix is a hardware-accelerated windowing system that can scroll windows without copying data. Amix is not supported on the later Amiga systems based on 68040 or 68060 processors.
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Other, still maintained, operating systems are available for the classic Amiga platform, including Linux and NetBSD. Both require a CPU with MMU such as the 68020 with 68851 or full versions of the 68030, 68040 or 68060. There is also a version of Linux for Amigas with PowerPC accelerator cards. Debian and Yellow Dog Linux can run on the AmigaOne.
There is an official, older version of OpenBSD. The last Amiga release is 3.2. MINIX 1.5.10 also runs on Amiga.
Emulating other systems.
The Amiga Sidecar is a complete IBM PC XT compatible computer contained in an expansion card. It was released by Commodore in 1986 and promoted as a way to run business software on the Amiga 1000.
Amiga software.
In the late 1980s and early 1990s the platform became particularly popular for gaming, demoscene activities and creative software uses. During this time commercial developers marketed a wide range of games and creative software, often developing titles simultaneously for the Atari ST due to the similar hardware architecture. Popular creative software included 3D rendering (ray-tracing) packages, bitmap graphics editors, desktop video software, software development packages and "tracker" music editors.
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Until the late 1990s the Amiga remained a popular platform for non-commercial software, often developed by enthusiasts, and much of which was freely redistributable. An on-line archive, Aminet, was created in 1991 and until the late-1990s was the largest public archive of software, art and documents for any platform.
Marketing.
The name "Amiga" was chosen by the developers from the Spanish word for a female friend, because they knew Spanish, and because it occurred before Apple and Atari alphabetically. It also conveyed the message that the Amiga computer line was "user friendly" as a pun or play on words.
The first official Amiga logo was a rainbow-colored double check mark. In later marketing material Commodore largely dropped the checkmark and used logos styled with various typefaces. Although it was never adopted as a trademark by Commodore, the "Boing Ball" has been synonymous with Amiga since its launch. It became an unofficial and enduring theme after a visually impressive animated demonstration at the 1984 Winter Consumer Electronics Show in January 1984 showing a checkered ball bouncing and rotating. Following Escom's purchase of Commodore in 1996, the Boing Ball theme was incorporated into a new logo.
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Early Commodore advertisements attempted to cast the computer as an all-purpose business machine, though the Amiga was most commercially successful as a home computer. Throughout the 1980s and early 1990s Commodore primarily placed advertising in computer magazines and occasionally in national newspapers and on television.
Legacy.
Since the demise of Commodore, various groups have marketed successors to the original Amiga line:
AmigaOS and MorphOS are commercial proprietary operating systems. AmigaOS 4, based on AmigaOS 3.1 source code with some parts of version 3.9, is developed by Hyperion Entertainment and runs on PowerPC based hardware. MorphOS, based on some parts of AROS source code, is developed by MorphOS Team and is continued on Apple and other PowerPC based hardware.
There is also AROS, a free and open source operating system (re-implementation of the AmigaOS 3.1 APIs), for Amiga 68k, x86 and ARM hardware (one version runs Linux-hosted on the Raspberry Pi). In particular, AROS for Amiga 68k hardware aims to create an open source Kickstart ROM replacement for emulation purpose and/or for use on real "classic" hardware.
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Magazines.
"Amiga Format" continued publication until 2000. "Amiga Active" was launched in 1999 and was published until 2001.
Several magazines are in publication today: Print magazine "Amiga Addict" started publication in 2020."Amiga Future", which is available in both English and German; "Bitplane.it", a bimonthly magazine in Italian; and "AmigaPower", a long-running French magazine.
Trade shows.
The Amiga continues to be popular enough that fans to support conferences such as Amiga37 which had over 50 vendors.
Uses.
The Amiga series of computers found a place in early computer graphic design and television presentation. Season 1 and part of season 2 of the television series "Babylon 5" were rendered in LightWave 3D on Amigas. Other television series using Amigas for special effects included "SeaQuest DSV" and "Max Headroom".
In addition, many celebrities and notable individuals have made use of the Amiga:
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Actinophryid
The actinophryids are an order of heliozoa, a polyphyletic array of stramenopiles, having a close relationship with pedinellids and "Ciliophrys". They are common in fresh water and occasionally found in marine and soil habitats. Actinophryids are unicellular and roughly spherical in shape, with many axopodia that radiate outward from the cell body. Axopodia are a type of pseudopodia that are supported by hundreds of microtubules arranged in interlocking spirals and forming a needle-like internal structure or axoneme. Small granules, extrusomes, that lie under the membrane of the body and axopodia capture flagellates, ciliates and small metazoa that make contact with the arms.
Description.
Actinophryids are largely aquatic protozoa with a spherical cell body and many needle-like axopodia. They resemble the shape of a sun due to this structure, which is the inspiration for their common name: heliozoa, or "sun-animalcules". Their bodies, without arms, range in size from a few tens of micrometers to slightly under a millimeter across.
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The outer region of cell body is often vacuolated. The endoplasm of actinophryids is less vacuolated than the outer layer, and a sharp boundary layer may be seen by light microscopy. The organisms can be either mononucleate, with a single, well defined nucleus in the center of the cell body, or multinucleate, with 10 or more nuclei located under the outer vacuolated layer of cytoplasm. The cytoplasm of actinophryids is often granular, similar to that of "Amoeba".
Actinophryid cells may fuse when feeding, creating larger aggregated organisms. Fine granules that occur just under the cell membrane are used up when food vacuoles form to enclose prey. Actinophryids may also form cysts when food is not readily available. A layer of siliceous plates is deposited under the cell membrane during the encystment process.
Contractile vacuoles are common in these organisms, which are presumed to use them to maintain body volume by expelling fluids to compensate for the entry of water by osmosis. Contractile vacuoles are visible as clear bulges from the surface of the cell body that slowly fill then rapidly deflate, expelling their contents into the environment.
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Axopodia.
The most distinctive characteristic of the actinophryids is their axopodia. These axopodia consist of a central, rigid rod which is coated in a thin layer of ectoplasm. In "Actinophrys" the axonemes end on the surface of the central nucleus, and in the multicellular "Actinosphaerium" they end at or near nuclei. The axonemes are composed of microtubules arranged in a double spiral pattern characteristic of the order. Due to their long, parallel construction, these microtubules demonstrate strong birefringence.
These axopodia are used for prey capture, in movement, cell fusion and perhaps division. They are stiff but may flex especially near their tips, and are highly dynamic, undergoing frequent construction and destruction. When used to collect prey items, two methods of capture have been noted, termed axopodial flow and rapid axopodial contraction. Axopodial flow involves the slow movement of a prey item along the surface of the axopod as the ectoplasm itself moves, while rapid axopodial contraction involves the collapse of the axoneme's microtubule structure. This behavior has been documented in many species, including "Actinosphaerium nucleofilum", "Actinophrys sol", and "Raphidiophrys contractilis". The rapid axopodial contraction occurs at high speed, often in excess of 5mm/s or tens of body lengths per second.
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The axopodial contractions have been shown to be highly sensitive to environmental factors such as temperature and pressure as well as chemical signals like Ca2+ and colchicine.
Reproduction.
Reproduction in actinophryids generally takes place via fission, where one parent cell divides into two or more daughter cells. For multinucleate heliozoa, this process is plasmotomic as the nuclei are not duplicated prior to division. It has been observed that reproduction appears to be a response to food scarcity, with an increased number of divisions following the removal of food and larger organisms during times of food excess.
Actinophryids also undergo autogamy during times of food scarcity. This is better described as genetic reorganization than reproduction, as the number of individuals produced is the same as the initial number. Nonetheless, it serves as a way to increase genetic diversity within an individual which may improve the likelihood of expressing favorable genetic traits.
Plastogamy has also been extensively documented in actinophryids, especially in multinucleate ones. "Actinosphaerium" were observed to combine freely without the combination of nuclei, and this process sometimes resulted in more or less individuals than originally combined. This process is not caused merely by contact between two individuals but can be caused by damage to the cell body.
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Cyst function and formation.
Under unfavourable conditions, some species will form a cyst. This is often the product of autogamy, in which case the cysts produced are zygotes. Cells undergoing this process withdraw their axopodia, adhere to the substrate, and take on an opaque and grayish appearance. This cyst then divides until only uninucleate cells remain. The cyst wall is thickly layered 7–8 times and includes gelatinous layers, layers of silica plates, and iron.
Taxonomy.
Originally placed in Heliozoa (Sarcodina), the actinophryids are now understood to be part of the stramenopiles. They are unrelated to centrohelid and desmothoracid heliozoa with which they had been previously classified.
There are several genera included within this classification. "Actinophrys" are smaller and have a single, central nucleus. Most have a cell body 40–50 micrometer in diameter with axopods around 100 μm in length, though this varies significantly. "Actinosphaerium" are several times larger, from 200 to 1000 μm in diameter, with many nuclei and are found exclusively in fresh water. A third genus, "Camptonema", has a debated status. It has been observed once and was treated as a junior subjective synonym of "Actinosphaerium" by Mikrjukov & Patterson in 2001, but as a valid genus by Cavalier-Smith & Scoble (2013). "Heliorapha" is a further debated taxon, it being a new generic vehicle for the species "azurina" that was initially assigned to the genus "Ciliophrys".
Classification.
According to the latest review of actinophryid classifications, they are organized into two suborders, three families and three genera.
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Abel Tasman
Abel Janszoon Tasman (; 160310 October 1659) was a Dutch seafarer and explorer, best known for his voyages of 1642 and 1644 in the service of the Dutch East India Company (VOC). He was the first European to reach New Zealand, which he named "Staten Landt". He was also the eponym of Tasmania.
Likely born in 1602 or 1603 in Lutjegast, Netherlands, Tasman started his career as a merchant seaman and became a skilled navigator. In 1633, he joined the VOC and sailed to Batavia, now Jakarta, Indonesia. He participated in several voyages, including one to Japan. In 1642, Tasman was appointed by the VOC to lead an expedition to explore the uncharted regions of the Southern Pacific Ocean. His mission was to discover new trade routes and to establish trade relations with the native inhabitants. After leaving Batavia, Tasman sailed westward to Mauritius, then south to the Roaring Forties, then eastward, and reached the coast of Tasmania, which he named Van Diemen's Land after his patron, Anthony van Diemen. He then sailed north east, and was the first European to discover the west coast of New Zealand, which he named "Staten Landt". It was later renamed "Nieuw Zeeland", after the Dutch province of Zeeland, by Joan Blaeu, official Dutch cartographer to the Dutch East India Company.
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Despite his achievements, Tasman's expedition was not entirely successful. The encounter with the Māori people on the South Island of New Zealand resulted in a violent confrontation, which left four of Tasman's men dead. He returned to Batavia without having made any significant contact with the native inhabitants or establishing any trade relations. Nonetheless, Tasman's expedition paved the way for further exploration and colonization of Australia and New Zealand by the British. Tasman continued to serve the Dutch East India Company until his death in 1659, leaving behind a legacy as one of the greatest explorers of his time.
Biography.
Early life.
Abel Tasman was likely born in 1602 or 1603 in Lutjegast, a village in the Province of Groningen. He married Claesgie Heyndrix, with whom he had a daughter named Claesjen. A proclamation of his second marriage, given in December 1631 at Amsterdam, describes him as a widower and sailor. On 27 December 1631 as a 28-year old seafarer living in Amsterdam, he married 21-year-old Jannetje Tjaers, of Palmstraat in Amsterdam.
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Relocation to the Dutch East Indies.
Uneducated, but employed by the Dutch East India Company (VOC), Tasman learned navigation and seamanship on the job. In 1634, he was appointed skipper of the "Mocha", and, under the command of Frans Valck, he went on a two-year voyage to the Maluku Islands.
Tasman sailed from Texel (Netherlands) to Batavia, now Jakarta, in 1633 taking the southern Brouwer Route. While based in Batavia, Tasman took part in a voyage to Seram Island (in what is now the Maluku Province in Indonesia) because the locals had sold spices to other European nationalities than the Dutch.
Tasman docked to find wood for repairs and was separated from the other ships; a fight broke out with local villagers and at least two of Tasman's men were killed.
By August 1637, Tasman had returned to Amsterdam, and in 1638 he signed on for another ten years and took his wife with him to Batavia via a six-month journey. On 25 March 1638, he tried to sell his property in the Jordaan, but the purchase was cancelled.
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He was second-in-command of a 1639 expedition of exploration into the north Pacific under Matthijs Quast. The fleet included the ships "Engel" and "Gracht" and reached Fort Zeelandia (Dutch Formosa) and Deshima (an artificial island off Nagasaki, Japan).
First major voyage.
In August 1642, the Council of the Indies, consisting of Antonie van Diemen, Cornelis van der Lijn, Joan Maetsuycker, Justus Schouten, Salomon Sweers, Cornelis Witsen, and Pieter Boreel in Batavia dispatched Tasman and Franchoijs Jacobszoon Visscher on a voyage of exploration to little-charted areas east of the Cape of Good Hope, west of Staten Land (near the Cape Horn of South America) and south of the Solomon Islands.
One of the objectives was to obtain knowledge of "all the totally unknown" Provinces of Beach. This was a purported yet phantom island said to have plentiful gold, which had appeared on European maps since the 15th century, as a result of an error in some editions of Marco Polo's works.
The expedition was to use two small ships, "Heemskerck" and "Zeehaen".
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Mauritius.
In accordance with Visscher's directions, Tasman sailed from Batavia on 14 August 1642 and arrived at Mauritius on 5 September 1642, according to the captain's journal. The reason for this was the crew could be fed well on the island; there was plenty of fresh water and timber to repair the ships. Tasman got the assistance of the governor Adriaan van der Stel.
Because of the prevailing winds, Mauritius was chosen as a turning point. After a four-week stay on the island, both ships left on 8 October using the Roaring Forties to sail east as fast as possible. (No one had gone as far as Pieter Nuyts in 1626/27.) On 7 November, snow and hail influenced the ship's council to alter course to a more north-easterly direction, with the intention of having the Solomon Islands as their destination.
Tasmania.
On 24 November 1642, Tasman reached and sighted the west coast of Tasmania, north of Macquarie Harbour. He named his discovery Van Diemen's Land, after Antonio van Diemen, Governor-General of the Dutch East Indies.
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Proceeding south, Tasman skirted the southern end of Tasmania and turned north-east. He then tried to work his two ships into Adventure Bay on the east coast of South Bruny Island, but he was blown out to sea by a storm. This area he named Storm Bay. Two days later, on 1 December, Tasman anchored to the north of Cape Frederick Hendrick just north of the Forestier Peninsula. On 2 December, two ship's boats under the command of the Pilot, Major Visscher, rowed through the Marion Narrows into Blackman Bay, and then west to the outflow of Boomer Creek where they gathered some edible "greens". Tasman named the bay, Frederick Hendrik Bay, which included the present North Bay, Marion Bay and what is now Blackman Bay. (Tasman's original naming, Frederick Henrick Bay, was mistakenly transferred to its present location by Marion Dufresne in 1772). The next day, an attempt was made to land in North Bay. However, because the sea was too rough, a ship's carpenter swam through the surf and planted the Dutch flag. Tasman then claimed formal possession of the land on 3 December 1642.
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For two more days, he continued to follow the east coast northward to see how far it went. When the land veered to the north-west at Eddystone Point, he tried to follow the coast line but his ships were suddenly hit by the Roaring Forties howling through Bass Strait. Tasman was on a mission to find the Southern Continent not more islands, so he abruptly turned away to the east and continued his continent-hunting.
New Zealand.
Tasman had intended to proceed in a northerly direction but as the wind was unfavourable he steered east. The expedition endured a rough voyage and in one of his diary entries Tasman claimed that his compass was the only thing that had kept him alive.
On 13 December 1642 Tasman and his crew became the first Europeans to reach New Zealand when they sighted the north-west coast of the South Island. Tasman named it "Staten Landt" "in honour of the States General" (Dutch parliament). He wrote, "it is possible that this land joins to the Staten Landt but it is uncertain", referring to Isla de los Estados, a landmass of the same name at the southern tip of South America, encountered by the Dutch navigator Jacob Le Maire in 1616. However, in 1643 Brouwer's expedition to Valdivia found out that Staaten Landt was separated by sea from the hypothetical Southern Land. Tasman continued: "We believe that this is the mainland coast of the unknown Southland." Tasman thought he had found the western side of the long-imagined "Terra Australis" that stretched across the Pacific to near the southern tip of South America. On 14 December 1642 Tasman's ships anchored 7 km offshore c. 20km south of Cape Foulwind near Greymouth. The ships were observed by Māori who named a place on this coast Tiropahi (the place were a large sailing ship was seen).
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After sailing north then east for five days, the expedition anchored about from the coast off what is now Golden Bay. A group of Māori paddled out in a waka (canoe) and attacked some sailors who were rowing between the two Dutch vessels. Four sailors were clubbed to death with patu. As Tasman sailed out of the bay he observed 22 waka near the shore, of which "eleven swarming with people came off towards us". The waka approached the "Zeehaen" which fired and hit a man in the largest waka holding a small white flag. Canister shot also hit the side of a waka. Archaeologist Ian Barber suggests that local Māori were trying to secure a cultivation field under ritual protection (tapu) where they believed the Dutch were attempting to land. December was at the mid-point of the locally important sweet potato/kūmara ("Ipomoea batatas") growing season. Tasman named the area "Murderers' Bay".
The expedition then sailed north, sighting Cook Strait, which separates the North and South Islands of New Zealand, and which it mistook for a bight and named "Zeehaen's Bight". Two names that the expedition gave to landmarks in the far north of New Zealand still endure: Cape Maria van Diemen and Three Kings Islands. ("Kaap Pieter Boreels" was renamed Cape Egmont by Captain James Cook 125 years later.)
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Return voyage.
En route back to Batavia, Tasman came across the Tongan archipelago on 20 January 1643. While passing the Fiji Islands Tasman's ships came close to being wrecked on the dangerous reefs of the north-eastern part of the Fiji group. He charted the eastern tip of Vanua Levu and Cikobia-i-Lau before making his way back into the open sea.
The expedition turned north-west towards New Guinea and arrived back in Batavia on 15 June 1643.
Second major voyage.
Tasman left Batavia on 30 January 1644 on his second voyage with three ships: "Limmen", "Zeemeeuw" and the tender "Braek". He followed the south coast of New Guinea eastwards in an attempt to find a passage to the eastern side of New Holland. However, he missed the Torres Strait between New Guinea and Australia, probably due to the numerous reefs and islands obscuring potential routes, and continued his voyage by following the shore of the Gulf of Carpentaria westwards along the north Australian coast. He mapped the north coast of Australia, making observations on New Holland and its people. He arrived back in Batavia in August 1644.
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From the point of view of the Dutch East India Company, Tasman's explorations were a disappointment: he had neither found a promising area for trade nor a useful new shipping route. Although Tasman was received courteously on his return, the company was upset that Tasman had not fully explored the lands he found, and decided that a more "persistent explorer" should be chosen for any future expeditions. For over a century, until the era of James Cook, Tasmania and New Zealand were not visited by Europeans; mainland Australia was visited, but usually only by accident.
Later life.
On 2 November 1644, Abel Tasman was appointed a member of the Council of Justice in Batavia. He went to Sumatra in 1646, and in August 1647 to Siam (now Thailand) with letters from the company to the King. In May 1648, he was in charge of an expedition sent to Manila to try to intercept and loot the Spanish silver ships coming from America, but he had no success and returned to Batavia in January 1649. In November 1649, he was charged and found guilty of having in the previous year hanged one of his men without trial, was suspended from his office of commander, fined, and made to pay compensation to the relatives of the sailor. On 5 January 1651, he was formally reinstated in his rank and spent his remaining years at Batavia. He was in good circumstances, being one of the larger landowners in the town. In 1653, he retired; at that time he owned 288 acres of land in Batavia and captained a small cargo ship, of which he was a part-owner.
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In April 1657, Tasman wrote his will and testament, describing himself as ill but not bedridden. Tasman died at Batavia on 10 October 1659 and was survived by his second wife and a daughter by his first wife. His property was divided between his wife and his daughter. In his will, he left 25 guilders to the poor of his village, Lutjegast.
Although Tasman's pilot, Frans Visscher, published "Memoir concerning the discovery of the South land" in 1642, Tasman's detailed journal was not published until 1898. Nevertheless, some of his charts and maps were in general circulation and used by subsequent explorers. The journal signed by Abel Tasman of the 1642 voyage is held in the Dutch National Archives at The Hague.
Legacy.
Tasman's ten-month voyage in 1642–43 had significant consequences. By circumnavigating Australia (albeit at a distance) Tasman proved that the small fifth continent was not joined to any larger sixth continent, such as the long-imagined Southern Continent. Further, Tasman's suggestion that New Zealand was the western side of that Southern Continent was seized upon by many European cartographers who, for the next century, depicted New Zealand as the west coast of a "Terra Australis" rising gradually from the waters around Tierra del Fuego. This theory was eventually disproved when Captain Cook circumnavigated New Zealand in 1769.
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Multiple places have been named after Tasman, including:
Also named after Tasman are:
His portrait has been on four New Zealand postage stamp issues, on a 1992 5 NZD coin, and on 1963, 1966 and 1985 Australian postage stamps.
In the Netherlands, many streets are named after him. In Lutjegast, the village where he was born, there is a museum dedicated to his life and travels.
Tasman's life was dramatised for radio in "Early in the Morning" (1946) a play by Ruth Park.
Portraits and depictions.
A drawing titled "Abel Janssen Tasman, Navigateur en Australie" is held by the State Library of New South Wales as part of "a portfolio of 26 ink drawings of 16th and 17th century Dutch admirals, navigators and governor-generals of the VOC". The portfolio was acquired at an art auction in The Hague in 1862. However, it is unclear if the drawing is of Tasman and its original source is unknown, although it has been said to resemble the work of Dutch engraver Jacobus Houbraken. The drawing has been assessed as having the "most reliable provenance" of any depiction of Tasman with "no strong reason to doubt that the drawing is not genuine".
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In 1948, the National Library of Australia acquired from Rex Nan Kivell a portrait purporting to depict Tasman with his wife and stepdaughter, which was attributed to Jacob Gerritsz. Cuyp and dated to 1637. In 2018 the painting was exhibited by the Groninger Museum in the Netherlands which identified it as "the only known portrait of the explorer". However, the Netherlands Institute for Art History has instead attributed the painting to Dirck van Santvoort and concluded that the painting does not depict Tasman and his family.
The provenance provided from Nan Kivell for the family portrait has been unable to be verified. Nan Kivell claimed that the portrait was passed down through the Springer family – relatives of Tasman's widow – and was sold at Christie's in 1877. However, Christie's records indicate that the portrait was not owned by the Springer family or associated with Tasman, and was instead sold as "Portrait of an astronomer" by "Anthonie Palamedes" [sic]. Nan Kivell additionally claimed that the portrait was sold at Christie's a second time in 1941, however no records exist to support this. A survey of portraits of Tasman published in 2019 concluded that the provenance was "either invented by Rex Nan Kivell or by the unnamed art dealer who sold it to Rex Nan Kivell", and that the painting "should therefore not be considered a portrait of Abel Tasman's family".
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Outside of the Nan Kivell painting, another purported portrait of Tasman was "discovered" in 1893 and eventually acquired by the Tasmanian government in 1976 for the Tasmanian Museum and Art Gallery (TMAG). The painting is unsigned and was attributed to Bartholomeus van der Helst at the time of its discovery, but this attribution was disputed by Dutch art historian Cornelis Hofstede de Groot and Alec Martin of Christie's. In 1985, TMAG curator Dan Gregg stated that "the painter of the life-sized portrait is unknown [...] there is some uncertainty as to whether the portrait is really of Tasman".
Tasman map.
Held within the collection of the State Library of New South Wales is the Tasman map, thought to have been drawn by Isaac Gilsemans, or completed under the supervision of Franz Jacobszoon Visscher. The map is also known as the Bonaparte map, as it was once owned by Prince Roland Bonaparte, the great-nephew of Napoleon. The map was completed sometime after 1644 and is based on the original charts drawn during Tasman's first and second voyages. As none of the journals or logs composed during Tasman's second voyage have survived, the Bonaparte map remains an important contemporary artefact of Tasman's voyage to the northern coast of the Australian continent.
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The Tasman map reveals the extent of understanding the Dutch had of the Australian continent at the time. The map includes the western and southern coasts of Australia, accidentally encountered by Dutch voyagers as they journeyed by way of the Cape of Good Hope to the VOC headquarters in Batavia. In addition, the map shows the tracks of Tasman's two voyages. Of his second voyage, the map shows the Banda Islands, the southern coast of New Guinea and much of the northern coast of Australia. However, the land areas adjacent to the Torres Strait are shown unexamined; this is despite Tasman having been given orders by VOC Council at Batavia to explore the possibility of a channel between New Guinea and the Australian continent.
There is debate as to the origin of the map. It is widely believed that the map was produced in Batavia; however, it has also been argued that the map was produced in Amsterdam. The authorship of the map has also been debated: while the map is commonly attributed to Tasman, it is now thought to have been the result of a collaboration, probably involving Franchoijs Visscher and Isaack Gilsemans, who took part in both of Tasman's voyages. Whether the map was produced in 1644 is also subject to debate, as a VOC company report in December 1644 suggested that at that time no maps showing Tasman's voyages were yet complete.
In 1943, a mosaic version of the map, composed of coloured brass and marble, was inlaid into the vestibule floor of the Mitchell Library in Sydney. The work was commissioned by the Principal Librarian William Ifould, and completed by the Melocco Brothers of Annandale, who also worked on the ANZAC War Memorial in Hyde Park and the crypt at St Mary's Cathedral, Sydney.
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Algebraic geometry
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems. Classically, it studies zeros of multivariate polynomials; the modern approach generalizes this in a few different aspects.
The fundamental objects of study in algebraic geometry are algebraic varieties, which are geometric manifestations of solutions of systems of polynomial equations. Examples of the most studied classes of algebraic varieties are lines, circles, parabolas, ellipses, hyperbolas, cubic curves like elliptic curves, and quartic curves like lemniscates and Cassini ovals. These are plane algebraic curves. A point of the plane lies on an algebraic curve if its coordinates satisfy a given polynomial equation. Basic questions involve the study of points of special interest like singular points, inflection points and points at infinity. More advanced questions involve the topology of the curve and the relationship between curves defined by different equations.
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Algebraic geometry occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex analysis, topology and number theory. As a study of systems of polynomial equations in several variables, the subject of algebraic geometry begins with finding specific solutions via equation solving, and then proceeds to understand the intrinsic properties of the totality of solutions of a system of equations. This understanding requires both conceptual theory and computational technique.
In the 20th century, algebraic geometry split into several subareas.
Much of the development of the mainstream of algebraic geometry in the 20th century occurred within an abstract algebraic framework, with increasing emphasis being placed on "intrinsic" properties of algebraic varieties not dependent on any particular way of embedding the variety in an ambient coordinate space; this parallels developments in topology, differential and complex geometry. One key achievement of this abstract algebraic geometry is Grothendieck's scheme theory which allows one to use sheaf theory to study algebraic varieties in a way which is very similar to its use in the study of differential and analytic manifolds. This is obtained by extending the notion of point: In classical algebraic geometry, a point of an affine variety may be identified, through Hilbert's Nullstellensatz, with a maximal ideal of the coordinate ring, while the points of the corresponding affine scheme are all prime ideals of this ring. This means that a point of such a scheme may be either a usual point or a subvariety. This approach also enables a unification of the language and the tools of classical algebraic geometry, mainly concerned with complex points, and of algebraic number theory. Wiles' proof of the longstanding conjecture called Fermat's Last Theorem is an example of the power of this approach.
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Basic notions.
Zeros of simultaneous polynomials.
In classical algebraic geometry, the main objects of interest are the vanishing sets of collections of polynomials, meaning the set of all points that simultaneously satisfy one or more polynomial equations. For instance, the two-dimensional sphere of radius 1 in three-dimensional Euclidean space R3 could be defined as the set of all points formula_1 with
A "slanted" circle in R3 can be defined as the set of all points formula_1 which satisfy the two polynomial equations
Affine varieties.
First we start with a field "k". In classical algebraic geometry, this field was always the complex numbers C, but many of the same results are true if we assume only that "k" is algebraically closed. We consider the affine space of dimension "n" over "k", denoted An("k") (or more simply A"n", when "k" is clear from the context). When one fixes a coordinate system, one may identify An("k") with "k""n". The purpose of not working with "k""n" is to emphasize that one "forgets" the vector space structure that "k"n carries.
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A function "f" : A"n" → A1 is said to be "polynomial" (or "regular") if it can be written as a polynomial, that is, if there is a polynomial "p" in "k"["x"1...,"x""n"] such that "f"("M") = "p"("t"1...,"t""n") for every point "M" with coordinates ("t"1...,"t""n") in A"n". The property of a function to be polynomial (or regular) does not depend on the choice of a coordinate system in A"n".
When a coordinate system is chosen, the regular functions on the affine "n"-space may be identified with the ring of polynomial functions in "n" variables over "k". Therefore, the set of the regular functions on A"n" is a ring, which is denoted "k"[A"n"].
We say that a polynomial "vanishes" at a point if evaluating it at that point gives zero. Let "S" be a set of polynomials in "k"[An]. The "vanishing set of S" (or "vanishing locus" or "zero set") is the set "V"("S") of all points in A"n" where every polynomial in "S" vanishes. Symbolically,
A subset of A"n" which is "V"("S"), for some "S", is called an "algebraic set". The "V" stands for "variety" (a specific type of algebraic set to be defined below).
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Given a subset "U" of A"n", can one recover the set of polynomials which generate it? If "U" is "any" subset of A"n", define "I"("U") to be the set of all polynomials whose vanishing set contains "U". The "I" stands for ideal: if two polynomials "f" and "g" both vanish on "U", then "f"+"g" vanishes on "U", and if "h" is any polynomial, then "hf" vanishes on "U", so "I"("U") is always an ideal of the polynomial ring "k"[A"n"].
Two natural questions to ask are:
The answer to the first question is provided by introducing the Zariski topology, a topology on A"n" whose closed sets are the algebraic sets, and which directly reflects the algebraic structure of "k"[A"n"]. Then "U" = "V"("I"("U")) if and only if "U" is an algebraic set or equivalently a Zariski-closed set. The answer to the second question is given by Hilbert's Nullstellensatz. In one of its forms, it says that "I"("V"("S")) is the radical of the ideal generated by "S". In more abstract language, there is a Galois connection, giving rise to two closure operators; they can be identified, and naturally play a basic role in the theory; the example is elaborated at Galois connection.
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For various reasons we may not always want to work with the entire ideal corresponding to an algebraic set "U". Hilbert's basis theorem implies that ideals in "k"[A"n"] are always finitely generated.
An algebraic set is called "irreducible" if it cannot be written as the union of two smaller algebraic sets. Any algebraic set is a finite union of irreducible algebraic sets and this decomposition is unique. Thus its elements are called the "irreducible components" of the algebraic set. An irreducible algebraic set is also called a "variety". It turns out that an algebraic set is a variety if and only if it may be defined as the vanishing set of a prime ideal of the polynomial ring.
Some authors do not make a clear distinction between algebraic sets and varieties and use "irreducible variety" to make the distinction when needed.
Regular functions.
Just as continuous functions are the natural maps on topological spaces and smooth functions are the natural maps on differentiable manifolds, there is a natural class of functions on an algebraic set, called "regular functions" or "polynomial functions". A regular function on an algebraic set "V" contained in A"n" is the restriction to "V" of a regular function on A"n". For an algebraic set defined on the field of the complex numbers, the regular functions are smooth and even analytic.
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It may seem unnaturally restrictive to require that a regular function always extend to the ambient space, but it is very similar to the situation in a normal topological space, where the Tietze extension theorem guarantees that a continuous function on a closed subset always extends to the ambient topological space.
Just as with the regular functions on affine space, the regular functions on "V" form a ring, which we denote by "k"["V"]. This ring is called the "coordinate ring of V".
Since regular functions on V come from regular functions on A"n", there is a relationship between the coordinate rings. Specifically, if a regular function on "V" is the restriction of two functions "f" and "g" in "k"[A"n"], then "f" − "g" is a polynomial function which is null on "V" and thus belongs to "I"("V"). Thus "k"["V"] may be identified with "k"[A"n"]/"I"("V").
Morphism of affine varieties.
Using regular functions from an affine variety to A1, we can define regular maps from one affine variety to another. First we will define a regular map from a variety into affine space: Let "V" be a variety contained in A"n". Choose "m" regular functions on "V", and call them "f"1, ..., "f""m". We define a "regular map" "f" from "V" to A"m" by letting . In other words, each "f""i" determines one coordinate of the range of "f".
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If "V"′ is a variety contained in A"m", we say that "f" is a "regular map" from "V" to "V"′ if the range of "f" is contained in "V"′.
The definition of the regular maps apply also to algebraic sets.
The regular maps are also called "morphisms", as they make the collection of all affine algebraic sets into a category, where the objects are the affine algebraic sets and the morphisms are the regular maps. The affine varieties is a subcategory of the category of the algebraic sets.
Given a regular map "g" from "V" to "V"′ and a regular function "f" of "k"["V"′], then . The map is a ring homomorphism from "k"["V"′] to "k"["V"]. Conversely, every ring homomorphism from "k"["V"′] to "k"["V"] defines a regular map from "V" to "V"′. This defines an equivalence of categories between the category of algebraic sets and the opposite category of the finitely generated reduced "k"-algebras. This equivalence is one of the starting points of scheme theory.
Rational function and birational equivalence.
In contrast to the preceding sections, this section concerns only varieties and not algebraic sets. On the other hand, the definitions extend naturally to projective varieties (next section), as an affine variety and its projective completion have the same field of functions.
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If "V" is an affine variety, its coordinate ring is an integral domain and has thus a field of fractions which is denoted "k"("V") and called the "field of the rational functions" on "V" or, shortly, the "function field" of "V". Its elements are the restrictions to "V" of the rational functions over the affine space containing "V". The domain of a rational function "f" is not "V" but the complement of the subvariety (a hypersurface) where the denominator of "f" vanishes.
As with regular maps, one may define a "rational map" from a variety "V" to a variety "V"'. As with the regular maps, the rational maps from "V" to "V"' may be identified to the field homomorphisms from "k"("V"') to "k"("V").
Two affine varieties are "birationally equivalent" if there are two rational functions between them which are inverse one to the other in the regions where both are defined. Equivalently, they are birationally equivalent if their function fields are isomorphic.
An affine variety is a "rational variety" if it is birationally equivalent to an affine space. This means that the variety admits a "rational parameterization", that is a parametrization with rational functions. For example, the circle of equation formula_7 is a rational curve, as it has the parametric equation
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which may also be viewed as a rational map from the line to the circle.
The problem of resolution of singularities is to know if every algebraic variety is birationally equivalent to a variety whose projective completion is nonsingular (see also smooth completion). It was solved in the affirmative in characteristic 0 by Heisuke Hironaka in 1964 and is yet unsolved in finite characteristic.
Projective variety.
Just as the formulas for the roots of second, third, and fourth degree polynomials suggest extending real numbers to the more algebraically complete setting of the complex numbers, many properties of algebraic varieties suggest extending affine space to a more geometrically complete projective space. Whereas the complex numbers are obtained by adding the number "i", a root of the polynomial , projective space is obtained by adding in appropriate points "at infinity", points where parallel lines may meet.
To see how this might come about, consider the variety . If we draw it, we get a parabola. As "x" goes to positive infinity, the slope of the line from the origin to the point ("x", "x"2) also goes to positive infinity. As "x" goes to negative infinity, the slope of the same line goes to negative infinity.
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Compare this to the variety "V"("y" − "x"3). This is a cubic curve. As "x" goes to positive infinity, the slope of the line from the origin to the point ("x", "x"3) goes to positive infinity just as before. But unlike before, as "x" goes to negative infinity, the slope of the same line goes to positive infinity as well; the exact opposite of the parabola. So the behavior "at infinity" of "V"("y" − "x"3) is different from the behavior "at infinity" of "V"("y" − "x"2).
The consideration of the "projective completion" of the two curves, which is their prolongation "at infinity" in the projective plane, allows us to quantify this difference: the point at infinity of the parabola is a regular point, whose tangent is the line at infinity, while the point at infinity of the cubic curve is a cusp. Also, both curves are rational, as they are parameterized by "x", and the Riemann-Roch theorem implies that the cubic curve must have a singularity, which must be at infinity, as all its points in the affine space are regular.
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Thus many of the properties of algebraic varieties, including birational equivalence and all the topological properties, depend on the behavior "at infinity" and so it is natural to study the varieties in projective space. Furthermore, the introduction of projective techniques made many theorems in algebraic geometry simpler and sharper: For example, Bézout's theorem on the number of intersection points between two varieties can be stated in its sharpest form only in projective space. For these reasons, projective space plays a fundamental role in algebraic geometry.
Nowadays, the "projective space" P"n" of dimension "n" is usually defined as the set of the lines passing through a point, considered as the origin, in the affine space of dimension , or equivalently to the set of the vector lines in a vector space of dimension . When a coordinate system has been chosen in the space of dimension , all the points of a line have the same set of coordinates, up to the multiplication by an element of "k". This defines the homogeneous coordinates of a point of P"n" as a sequence of elements of the base field "k", defined up to the multiplication by a nonzero element of "k" (the same for the whole sequence).
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A polynomial in variables vanishes at all points of a line passing through the origin if and only if it is homogeneous. In this case, one says that the polynomial "vanishes" at the corresponding point of P"n". This allows us to define a "projective algebraic set" in P"n" as the set , where a finite set of homogeneous polynomials vanishes. Like for affine algebraic sets, there is a bijection between the projective algebraic sets and the reduced homogeneous ideals which define them. The "projective varieties" are the projective algebraic sets whose defining ideal is prime. In other words, a projective variety is a projective algebraic set, whose homogeneous coordinate ring is an integral domain, the "projective coordinates ring" being defined as the quotient of the graded ring or the polynomials in variables by the homogeneous (reduced) ideal defining the variety. Every projective algebraic set may be uniquely decomposed into a finite union of projective varieties.
The only regular functions which may be defined properly on a projective variety are the constant functions. Thus this notion is not used in projective situations. On the other hand, the "field of the rational functions" or "function field " is a useful notion, which, similarly to the affine case, is defined as the set of the quotients of two homogeneous elements of the same degree in the homogeneous coordinate ring.
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Real algebraic geometry.
Real algebraic geometry is the study of real algebraic varieties.
The fact that the field of the real numbers is an ordered field cannot be ignored in such a study. For example, the curve of equation formula_10 is a circle if formula_11, but has no real points if formula_12. Real algebraic geometry also investigates, more broadly, "semi-algebraic sets", which are the solutions of systems of polynomial inequalities. For example, neither branch of the hyperbola of equation formula_13 is a real algebraic variety. However, the branch in the first quadrant is a semi-algebraic set defined by formula_14 and formula_15.
One open problem in real algebraic geometry is the following part of Hilbert's sixteenth problem: Decide which respective positions are possible for the ovals of a nonsingular plane curve of degree 8.
Computational algebraic geometry.
One may date the origin of computational algebraic geometry to meeting EUROSAM'79 (International Symposium on Symbolic and Algebraic Manipulation) held at Marseille, France, in June 1979. At this meeting,
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Since then, most results in this area are related to one or several of these items either by using or improving one of these algorithms, or by finding algorithms whose complexity is simply exponential in the number of the variables.
A body of mathematical theory complementary to symbolic methods called numerical algebraic geometry has been developed over the last several decades. The main computational method is homotopy continuation. This supports, for example, a model of floating point computation for solving problems of algebraic geometry.
Gröbner basis.
A Gröbner basis is a system of generators of a polynomial ideal whose computation allows the deduction of many properties of the affine algebraic variety defined by the ideal.
Given an ideal "I" defining an algebraic set "V":
Gröbner basis computations do not allow one to compute directly the primary decomposition of "I" nor the prime ideals defining the irreducible components of "V", but most algorithms for this involve Gröbner basis computation. The algorithms which are not based on Gröbner bases use regular chains but may need Gröbner bases in some exceptional situations.
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Gröbner bases are deemed to be difficult to compute. In fact they may contain, in the worst case, polynomials whose degree is doubly exponential in the number of variables and a number of polynomials which is also doubly exponential. However, this is only a worst case complexity, and the complexity bound of Lazard's algorithm of 1979 may frequently apply. Faugère F5 algorithm realizes this complexity, as it may be viewed as an improvement of Lazard's 1979 algorithm. It follows that the best implementations allow one to compute almost routinely with algebraic sets of degree more than 100. This means that, presently, the difficulty of computing a Gröbner basis is strongly related to the intrinsic difficulty of the problem.
Cylindrical algebraic decomposition (CAD).
CAD is an algorithm which was introduced in 1973 by G. Collins to implement with an acceptable complexity the Tarski–Seidenberg theorem on quantifier elimination over the real numbers.
This theorem concerns the formulas of the first-order logic whose atomic formulas are polynomial equalities or inequalities between polynomials with real coefficients. These formulas are thus the formulas which may be constructed from the atomic formulas by the logical operators "and" (∧), "or" (∨), "not" (¬), "for all" (∀) and "exists" (∃). Tarski's theorem asserts that, from such a formula, one may compute an equivalent formula without quantifier (∀, ∃).
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The complexity of CAD is doubly exponential in the number of variables. This means that CAD allows, in theory, to solve every problem of real algebraic geometry which may be expressed by such a formula, that is almost every problem concerning explicitly given varieties and semi-algebraic sets.
While Gröbner basis computation has doubly exponential complexity only in rare cases, CAD has almost always this high complexity. This implies that, unless if most polynomials appearing in the input are linear, it may not solve problems with more than four variables.
Since 1973, most of the research on this subject is devoted either to improving CAD or finding alternative algorithms in special cases of general interest.
As an example of the state of art, there are efficient algorithms to find at least a point in every connected component of a semi-algebraic set, and thus to test if a semi-algebraic set is empty. On the other hand, CAD is yet, in practice, the best algorithm to count the number of connected components.
Asymptotic complexity vs. practical efficiency.
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The basic general algorithms of computational geometry have a double exponential worst case complexity. More precisely, if "d" is the maximal degree of the input polynomials and "n" the number of variables, their complexity is at most formula_16 for some constant "c", and, for some inputs, the complexity is at least formula_17 for another constant "c"′.
During the last 20 years of the 20th century, various algorithms have been introduced to solve specific subproblems with a better complexity. Most of these algorithms have a complexity formula_18.
Among these algorithms which solve a sub problem of the problems solved by Gröbner bases, one may cite "testing if an affine variety is empty" and "solving nonhomogeneous polynomial systems which have a finite number of solutions." Such algorithms are rarely implemented because, on most entries Faugère's F4 and F5 algorithms have a better practical efficiency and probably a similar or better complexity ("probably" because the evaluation of the complexity of Gröbner basis algorithms on a particular class of entries is a difficult task which has been done only in a few special cases).
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The main algorithms of real algebraic geometry which solve a problem solved by CAD are related to the topology of semi-algebraic sets. One may cite "counting the number of connected components", "testing if two points are in the same components" or "computing a Whitney stratification of a real algebraic set". They have a complexity of
formula_18, but the constant involved by "O" notation is so high that using them to solve any nontrivial problem effectively solved by CAD, is impossible even if one could use all the existing computing power in the world. Therefore, these algorithms have never been implemented and this is an active research area to search for algorithms with have together a good asymptotic complexity and a good practical efficiency.
Abstract modern viewpoint.
The modern approaches to algebraic geometry redefine and effectively extend the range of basic objects in various levels of generality to schemes, formal schemes, ind-schemes, algebraic spaces, algebraic stacks and so on. The need for this arises already from the useful ideas within theory of varieties, e.g. the formal functions of Zariski can be accommodated by introducing nilpotent elements in structure rings; considering spaces of loops and arcs, constructing quotients by group actions and developing formal grounds for natural intersection theory and deformation theory lead to some of the further extensions.
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Most remarkably, in the early 1960s, algebraic varieties were subsumed into Alexander Grothendieck's concept of a scheme. Their local objects are affine schemes or prime spectra which are locally ringed spaces which form a category which is antiequivalent to the category of commutative unital rings, extending the duality between the category of affine algebraic varieties over a field "k", and the category of finitely generated reduced "k"-algebras. The gluing is along Zariski topology; one can glue within the category of locally ringed spaces, but also, using the Yoneda embedding, within the more abstract category of presheaves of sets over the category of affine schemes. The Zariski topology in the set theoretic sense is then replaced by a Grothendieck topology. Grothendieck introduced Grothendieck topologies having in mind more exotic but geometrically finer and more sensitive examples than the crude Zariski topology, namely the étale topology, and the two flat Grothendieck topologies: fppf and fpqc; nowadays some other examples became prominent including Nisnevich topology. Sheaves can be furthermore generalized to stacks in the sense of Grothendieck, usually with some additional representability conditions leading to Artin stacks and, even finer, Deligne–Mumford stacks, both often called algebraic stacks.
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Sometimes other algebraic sites replace the category of affine schemes. For example, Nikolai Durov has introduced commutative algebraic monads as a generalization of local objects in a generalized algebraic geometry. Versions of a tropical geometry, of an absolute geometry over a field of one element and an algebraic analogue of Arakelov's geometry were realized in this setup.
Another formal generalization is possible to universal algebraic geometry in which every variety of algebras has its own algebraic geometry. The term "variety of algebras" should not be confused with "algebraic variety".
The language of schemes, stacks and generalizations has proved to be a valuable way of dealing with geometric concepts and became cornerstones of modern algebraic geometry.
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History.
Before the 16th century.
Some of the roots of algebraic geometry date back to the work of the Hellenistic Greeks from the 5th century BC. The Delian problem, for instance, was to construct a length "x" so that the cube of side "x" contained the same volume as the rectangular box "a"2"b" for given sides "a" and "b". Menaechmus () considered the problem geometrically by intersecting the pair of plane conics "ay" = "x"2 and "xy" = "ab". In the 3rd century BC, Archimedes and Apollonius systematically studied additional problems on conic sections using coordinates. Apollonius in the Conics further developed a method that is so similar to analytic geometry that his work is sometimes thought to have anticipated the work of Descartes by some 1800 years. His application of reference lines, a diameter and a tangent is essentially no different from our modern use of a coordinate frame, where the distances measured along the diameter from the point of tangency are the abscissas, and the segments parallel to the tangent and intercepted between the axis and the curve are the ordinates. He further developed relations between the abscissas and the corresponding coordinates using geometric methods like using parabolas and curves. Medieval mathematicians, including Omar Khayyam, Leonardo of Pisa, Gersonides and Nicole Oresme in the Medieval Period, solved certain cubic and quadratic equations by purely algebraic means and then interpreted the results geometrically. The Persian mathematician Omar Khayyám (born 1048 AD) believed that there was a relationship between arithmetic, algebra and geometry. This was criticized by Jeffrey Oaks, who claims that the study of curves by means of equations originated with Descartes in the seventeenth century.
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Renaissance.
Such techniques of applying geometrical constructions to algebraic problems were also adopted by a number of Renaissance mathematicians such as Gerolamo Cardano and Niccolò Fontana "Tartaglia" on their studies of the cubic equation. The geometrical approach to construction problems, rather than the algebraic one, was favored by most 16th and 17th century mathematicians, notably Blaise Pascal who argued against the use of algebraic and analytical methods in geometry. The French mathematicians Franciscus Vieta and later René Descartes and Pierre de Fermat revolutionized the conventional way of thinking about construction problems through the introduction of coordinate geometry. They were interested primarily in the properties of "algebraic curves", such as those defined by Diophantine equations (in the case of Fermat), and the algebraic reformulation of the classical Greek works on conics and cubics (in the case of Descartes).
During the same period, Blaise Pascal and Gérard Desargues approached geometry from a different perspective, developing the synthetic notions of projective geometry. Pascal and Desargues also studied curves, but from the purely geometrical point of view: the analog of the Greek "ruler and compass construction". Ultimately, the analytic geometry of Descartes and Fermat won out, for it supplied the 18th century mathematicians with concrete quantitative tools needed to study physical problems using the new calculus of Newton and Leibniz. However, by the end of the 18th century, most of the algebraic character of coordinate geometry was subsumed by the "calculus of infinitesimals" of Lagrange and Euler.
19th and early 20th century.
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It took the simultaneous 19th century developments of non-Euclidean geometry and Abelian integrals in order to bring the old algebraic ideas back into the geometrical fold. The first of these new developments was seized up by Edmond Laguerre and Arthur Cayley, who attempted to ascertain the generalized metric properties of projective space. Cayley introduced the idea of "homogeneous polynomial forms", and more specifically quadratic forms, on projective space. Subsequently, Felix Klein studied projective geometry (along with other types of geometry) from the viewpoint that the geometry on a space is encoded in a certain class of transformations on the space. By the end of the 19th century, projective geometers were studying more general kinds of transformations on figures in projective space. Rather than the projective linear transformations which were normally regarded as giving the fundamental Kleinian geometry on projective space, they concerned themselves also with the higher degree birational transformations. This weaker notion of congruence would later lead members of the 20th century Italian school of algebraic geometry to classify algebraic surfaces up to birational isomorphism.
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The second early 19th century development, that of Abelian integrals, would lead Bernhard Riemann to the development of Riemann surfaces.
In the same period began the algebraization of the algebraic geometry through commutative algebra. The prominent results in this direction are Hilbert's basis theorem and Hilbert's Nullstellensatz, which are the basis of the connection between algebraic geometry and commutative algebra, and Macaulay's multivariate resultant, which is the basis of elimination theory. Probably because of the size of the computation which is implied by multivariate resultants, elimination theory was forgotten during the middle of the 20th century until it was renewed by singularity theory and computational algebraic geometry.
20th century.
B. L. van der Waerden, Oscar Zariski and André Weil developed a foundation for algebraic geometry based on contemporary commutative algebra, including valuation theory and the theory of ideals. One of the goals was to give a rigorous framework for proving the results of the Italian school of algebraic geometry. In particular, this school used systematically the notion of generic point without any precise definition, which was first given by these authors during the 1930s.
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In the 1950s and 1960s, Jean-Pierre Serre and Alexander Grothendieck recast the foundations making use of sheaf theory. Later, from about 1960, and largely led by Grothendieck, the idea of schemes was worked out, in conjunction with a very refined apparatus of homological techniques. After a decade of rapid development the field stabilized in the 1970s, and new applications were made, both to number theory and to more classical geometric questions on algebraic varieties, singularities, moduli, and formal moduli.
An important class of varieties, not easily understood directly from their defining equations, are the abelian varieties, which are the projective varieties whose points form an abelian group. The prototypical examples are the elliptic curves, which have a rich theory. They were instrumental in the proof of Fermat's Last Theorem and are also used in elliptic-curve cryptography.
In parallel with the abstract trend of the algebraic geometry, which is concerned with general statements about varieties, methods for effective computation with concretely-given varieties have also been developed, which lead to the new area of computational algebraic geometry. One of the founding methods of this area is the theory of Gröbner bases, introduced by Bruno Buchberger in 1965. Another founding method, more specially devoted to real algebraic geometry, is the cylindrical algebraic decomposition, introduced by George E. Collins in 1973.
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See also: derived algebraic geometry.
Analytic geometry.
An analytic variety over the field of real or complex numbers is defined locally as the set of common solutions of several equations involving analytic functions. It is analogous to the concept of algebraic variety in that it carries a structure sheaf of analytic functions instead of regular functions. Any complex manifold is a complex analytic variety. Since analytic varieties may have singular points, not all complex analytic varieties are manifolds. Over a non-archimedean field analytic geometry is studied via rigid analytic spaces.
Modern analytic geometry over the field of complex numbers is closely related to complex algebraic geometry, as has been shown by Jean-Pierre Serre in his paper "GAGA", the name of which is French for "Algebraic geometry and analytic geometry". The GAGA results over the field of complex numbers may be extended to rigid analytic spaces over non-archimedean fields.
Applications.
Algebraic geometry now finds applications in statistics, control theory, robotics, error-correcting codes, phylogenetics and geometric modelling. There are also connections to string theory, game theory, graph matchings, solitons and integer programming.
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Austin, Texas
Austin ( ) is the capital city of the U.S. state of Texas. It is the county seat and most populous city of Travis County, with portions extending into Hays and Williamson counties. Incorporated on December 27, 1839, it is the 26th-largest metropolitan area in the United States, the 12th-most populous city in the United States, the fourth-most populous city in the state after Houston, San Antonio, and Dallas, and the second-most populous state capital city after Phoenix, Arizona. It has been one of the fastest growing large cities in the United States since 2010. Downtown Austin and Downtown San Antonio are approximately apart, and both fall along the I-35 corridor. This combined metropolitan region of San Antonio–Austin has approximately 5 million people. Austin is the southernmost state capital in the contiguous United States and is considered a Gamma + level global city as categorized by the Globalization and World Cities Research Network.
As of the 2020 census, Austin had a population of 961,855. The city is the cultural and economic center of the metropolitan statistical area, which had an estimated population of 2,473,275 as of July 1, 2023. Located in within the greater Texas Hill Country, it is home to numerous lakes, rivers, and waterways, including Lady Bird Lake and Lake Travis on the Colorado River, Barton Springs, McKinney Falls, and Lake Walter E. Long.
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Residents of Austin are known as Austinites. They include a diverse mix of government employees, college students, musicians, high-tech workers, and blue-collar workers. The city's official slogan promotes Austin as "The Live Music Capital of the World", a reference to the city's many musicians and live music venues, as well as the long-running PBS TV concert series "Austin City Limits". Austin is the site of South by Southwest (SXSW), an annual conglomeration of parallel film, interactive media, and music festivals. The city also adopted "Silicon Hills" as a nickname in the 1990s due to a rapid influx of technology and development companies. In recent years, some Austinites have adopted the unofficial slogan "Keep Austin Weird", which refers to the desire to protect small, unique, and local businesses from being overrun by large corporations. Since the late 19th century, Austin has also been known as the "City of the Violet Crown", because of the colorful glow of light across the hills just after sunset.
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History.
Austin, Travis County and Williamson County have been the site of human habitation since at least 9200 BC. The area's earliest known inhabitants lived during the late Pleistocene (Ice Age) and are linked to the Clovis culture around 9200 BC (over 11,200 years ago), based on evidence found throughout the area and documented at the much-studied Gault Site, midway between Georgetown and Fort Cavazos.
When settlers arrived from Europe, the Tonkawa tribe inhabited the area. The Comanches and Lipan Apaches were also known to travel through the area. Spanish colonists, including the Espinosa-Olivares-Aguirre expedition, traveled through the area, though few permanent settlements were created for some time. In 1730, three Catholic missions from East Texas were combined and reestablished as one mission on the south side of the Colorado River, in what is now Zilker Park, in Austin. The mission was in this area for only about seven months, then was moved to San Antonio de Béxar and split into three missions.
During the 1830s, pioneers began to settle the area in central Austin along the Colorado River. Spanish forts were established in what are now Bastrop and San Marcos. Following Mexico's independence, new settlements were established in Central Texas.
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In 1835–1836, Texans fought and won independence from Mexico. Texas thus became an independent country with its own president, congress, and monetary system. In 1839, the Texas Congress formed a commission to seek a site for the new capital of the Republic of Texas to replace Houston. When he was Vice President of Texas, Mirabeau B. Lamar had visited the area during a buffalo-hunting expedition between 1837 and 1838. He advised the commissioners to consider the area on the north bank of the Colorado River (near the present-day Congress Avenue Bridge), noting the area's hills, waterways, and pleasant surroundings. It was seen as a convenient crossroads for trade routes between Santa Fe and Galveston Bay, as well as routes between Northern Mexico and the Red River. In 1839, the site was chosen, and briefly incorporated under the name "Waterloo". Shortly afterward, the name was changed to Austin in honor of Stephen F. Austin, the "Father of Texas" and the republic's first secretary of state.
The city grew throughout the 19th century and became a center for government and education with the construction of the Texas State Capitol and the University of Texas at Austin.
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Edwin Waller was picked by Lamar to survey the village and draft a plan laying out the new capital. The original site was narrowed to that fronted the Colorado River between two creeks, Shoal Creek and Waller Creek, which was later named in his honor. Waller and a team of surveyors developed Austin's first city plan, commonly known as the Waller Plan, dividing the site into a 14-block grid plan bisected by a broad north–south thoroughfare, Congress Avenue, running up from the river to Capital Square, where the new Texas State Capitol was to be constructed. A temporary one-story capitol was erected on the corner of Colorado and 8th Streets. On August 1, 1839, the first auction of 217 out of 306 lots total was held. The Waller Plan designed and surveyed now forms the basis of downtown Austin.
In 1840, a series of conflicts between the Texas Rangers and the Comanches, known as the Council House Fight and the Battle of Plum Creek, pushed the Comanches westward, mostly ending conflicts in Central Texas. Settlement in the area began to expand quickly. Travis County was established in 1840, and the surrounding counties were mostly established within the next two decades.
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Initially, the new capital thrived but Lamar's political enemy, Sam Houston, used two Mexican army incursions to San Antonio as an excuse to move the government. Sam Houston fought bitterly against Lamar's decision to establish the capital in such a remote wilderness. The men and women who traveled mainly from Houston to conduct government business were intensely disappointed as well. By 1840, the population had risen to 856, nearly half of whom fled Austin when Congress recessed. The resident African American population listed in January of this same year was 176. The fear of Austin's proximity to the Indians and Mexico, which still considered Texas a part of their land, created an immense motive for Sam Houston, the first and third President of the Republic of Texas, to relocate the capital once again in 1841. Upon threats of Mexican troops in Texas, Houston raided the Land Office to transfer all official documents to Houston for safe keeping in what was later known as the Archive War, but the people of Austin would not allow this unaccompanied decision to be executed. The documents stayed, but the capital would temporarily move from Austin to Houston to Washington-on-the-Brazos. Without the governmental body, Austin's population declined to a low of only a few hundred people throughout the early 1840s. The voting by the fourth President of the Republic, Anson Jones, and Congress, who reconvened in Austin in 1845, settled the issue to keep Austin the seat of government, as well as annex the Republic of Texas into the United States.
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In 1860, 38% of Travis County residents were slaves. In 1861, with the outbreak of the American Civil War, voters in Austin and other Central Texas communities voted against secession. However, as the war progressed and fears of attack by Union forces increased, Austin contributed hundreds of men to the Confederate forces. The African American population of Austin swelled dramatically after the enforcement of the Emancipation Proclamation in Texas by Union General Gordon Granger at Galveston, in an event commemorated as Juneteenth. Black communities such as Wheatville, Pleasant Hill, and Clarksville were established, with Clarksville being the oldest surviving freedomtown ‒ the original post-Civil War settlements founded by former African-American slaves ‒ west of the Mississippi River. In 1870, blacks made up 36.5% of Austin's population.
The postwar period saw dramatic population and economic growth. The opening of the Houston and Texas Central Railway (H&TC) in 1871 turned Austin into the major trading center for the region, with the ability to transport both cotton and cattle. The Missouri, Kansas & Texas (MKT) line followed close behind. Austin was also the terminus of the southernmost leg of the Chisholm Trail, and "drovers" pushed cattle north to the railroad. Cotton was one of the few crops produced locally for export, and a cotton gin engine was located downtown near the trains for "ginning" cotton of its seeds and turning the product into bales for shipment. However, as other new railroads were built through the region in the 1870s, Austin began to lose its primacy in trade to the surrounding communities. In addition, the areas east of Austin took over cattle and cotton production from Austin, especially in towns like Hutto and Taylor that sit over the blackland prairie, with its deep, rich soils for producing cotton and hay.
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In September 1881, Austin public schools held their first classes. The same year, Tillotson Collegiate and Normal Institute (now part of Huston–Tillotson University) opened its doors. The University of Texas held its first classes in 1883, although classes had been held in the original wooden state capitol for four years before.
During the 1880s, Austin gained new prominence as the state capitol building was completed in 1888 and claimed as the seventh largest building in the world. In the late 19th century, Austin expanded its city limits to more than three times its former area, and the first granite dam was built on the Colorado River to power a new street car line and the new "moon towers". The first dam washed away in a flood on April 7, 1900.
In the late 1920s and 1930s, Austin implemented the 1928 Austin city plan through a series of civic development and beautification projects that created much of the city's infrastructure and many of its parks. In addition, the state legislature established the Lower Colorado River Authority (LCRA) that, along with the city of Austin, created the system of dams along the Colorado River to form the Highland Lakes. These projects were enabled in large part because the Public Works Administration provided Austin with greater funding for municipal construction projects than other Texas cities.
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During the early 20th century, a three-way system of social segregation emerged in Austin, with Anglos, African Americans and Mexicans being separated by custom or law in most aspects of life, including housing, health care, and education. Deed restrictions also played an important role in residential segregation. After 1935 most housing deeds prohibited African Americans (and sometimes other nonwhite groups) from using land. Combined with the system of segregated public services, racial segregation increased in Austin during the first half of the twentieth century, with African Americans and Mexicans experiencing high levels of discrimination and social marginalization.
In 1940, the destroyed granite dam on the Colorado River was finally replaced by a hollow concrete dam that formed Lake McDonald (now called Lake Austin) and which has withstood all floods since. In addition, the much larger Mansfield Dam was built by the LCRA upstream of Austin to form Lake Travis, a flood-control reservoir.
In the early 20th century, the Texas Oil Boom took hold, creating tremendous economic opportunities in Southeast Texas and North Texas. The growth generated by this boom largely passed by Austin at first, with the city slipping from fourth largest to tenth largest in Texas between 1880 and 1920.
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After a severe lull in economic growth from the Great Depression, Austin resumed its steady development. Following the mid-20th century, Austin became established as one of Texas' major metropolitan centers. In 1970, the U.S. Census Bureau reported Austin's population as 14.5% Hispanic, 11.9% black, and 73.4% non-Hispanic white. In the late 20th century, Austin emerged as an important high tech center for semiconductors and software. The University of Texas at Austin emerged as a major university.
The 1970s saw Austin's emergence in the national music scene, with local artists such as Willie Nelson, Asleep at the Wheel, and Stevie Ray Vaughan and iconic music venues such as the Armadillo World Headquarters. Over time, the long-running television program "Austin City Limits", its namesake Austin City Limits Festival, and the South by Southwest music festival solidified the city's place in the music industry.
Geography.
Austin, the southernmost state capital of the contiguous 48 states, is located in Central Texas on the Colorado River. Austin is northwest of Houston, south of Dallas and northeast of San Antonio.
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Austin occupies a total area of . Approximately of this area is water. Austin is situated at the foot of the Balcones Escarpment, on the Colorado River, with three artificial lakes within the city limits: Lady Bird Lake (formerly known as Town Lake), Lake Austin (both created by dams along the Colorado River), and Lake Walter E. Long that is partly used for cooling water for the Decker Power Plant. Mansfield Dam and the foot of Lake Travis are located within the city's limits. Lady Bird Lake, Lake Austin, and Lake Travis are each on the Colorado River.
The elevation of Austin varies from to approximately above sea level. Due to the fact it straddles the Balcones Fault, much of the eastern part of the city is flat, with heavy clay and loam soils, whereas the western part and western suburbs consist of rolling hills on the edge of the Texas Hill Country. Because the hills to the west are primarily limestone rock with a thin covering of topsoil, portions of the city are frequently subjected to flash floods from the runoff caused by thunderstorms. To help control this runoff and to generate hydroelectric power, the Lower Colorado River Authority operates a series of dams that form the Texas Highland Lakes. The lakes also provide venues for boating, swimming, and other forms of recreation within several parks on the lake shores.
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Austin is located at the intersection of four major ecological regions, and is consequently a temperate-to-hot green oasis with a highly variable climate having some characteristics of the desert, the tropics, and a wetter climate. The area is very diverse ecologically and biologically, and is home to a variety of animals and plants. Notably, the area is home to many types of wildflowers that blossom throughout the year but especially in the spring. This includes the popular bluebonnets, some planted by "Lady Bird" Johnson, wife of former President Lyndon B. Johnson.
The soils of Austin range from shallow, gravelly clay loams over limestone in the western outskirts to deep, fine sandy loams, silty clay loams, silty clays or clays in the city's eastern part. Some of the clays have pronounced shrink-swell properties and are difficult to work under most moisture conditions. Many of Austin's soils, especially the clay-rich types, are slightly to moderately alkaline and have free calcium carbonate.
Cityscape.
Austin's skyline historically was modest, dominated by the Texas State Capitol and the University of Texas Main Building. However, since the 2000s, many new high-rise towers have been constructed. Austin is currently undergoing a skyscraper boom, which includes recent construction on new office, hotel and residential buildings. Downtown's buildings are somewhat spread out, partly due to a set of zoning restrictions that preserve the view of the Texas State Capitol from various locations around Austin, known as the Capitol View Corridors.
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At night, parts of Austin are lit by "artificial moonlight" from moonlight towers built to illuminate the central part of the city. The moonlight towers were built in the late 19th century and are now recognized as historic landmarks. Only 15 of the 31 original innovative towers remain standing in Austin, but none remain in any of the other cities where they were installed. The towers are featured in the 1993 film "Dazed and Confused".
In December 2023, amid rising home prices, the Austin City Council loosened the city's zoning rules to permit by-right development of triplexes on each lot and loosened restrictions on tiny homes.
Downtown.
The central business district of Austin is home to the tallest condo towers in the state, with The Independent (58 stories and tall) and The Austonian (topping out at 56 floors and tall). The Independent became the tallest all-residential building in the U.S. west of Chicago when topped out in 2018. In 2005, then-Mayor Will Wynn set out a goal of having 25,000 people living downtown by 2015. Although downtown's growth did not meet this goal, downtown's residential population did surge from an estimated 5,000 in 2005 to 12,000 in 2015. The skyline has drastically changed in recent years, and the residential real estate market has remained relatively strong. , there were 31 high rise projects either under construction, approved or planned to be completed in Austin's downtown core between 2017 and 2020. Sixteen of those were set to rise above tall, including four above 600', and eight above 500'. An additional 15 towers were slated to stand between 300' and 399' tall.
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Climate.
Austin is located within the middle of a unique, narrow transitional zone between the dry deserts of the American Southwest and the lush, green, more humid regions of the American Southeast. Its climate, topography, and vegetation share characteristics of both. Officially, Austin has a humid subtropical climate ("Cfa" under the Köppen climate classification, "Cfhl" under the Trewartha climate classification). This climate is typified by long, very hot summers, short, mild winters, and warm to hot spring and fall seasons in-between. Austin averages of annual rainfall distributed mostly evenly throughout the year, though spring and fall are the wettest seasons. Sunshine is common during all seasons, with 2,650 hours, or 60.3% of the possible total, of bright sunshine per year.
Summers in Austin are very hot, with average July and August highs frequently reaching the high-90s (34–36 °C) or above. Highs reach on 123 days per year, of which 29 days reach ; all years in the 1991-2020 period recorded at least 1 day of the latter. The average daytime high is or warmer between March 1 and November 21, rising to or warmer between April 14 and October 24, and reaching or warmer between May 30 and September 18. The highest ever recorded temperature was occurring on September 5, 2000, and August 28, 2011. An uncommon characteristic of Austin's climate is its highly variable humidity, which fluctuates frequently depending on the shifting patterns of air flow and wind direction. It is common for a lengthy series of warm, dry, low-humidity days to be occasionally interrupted by very warm and humid days, and vice versa. Humidity rises with winds from the east or southeast, when the air drifts inland from the Gulf of Mexico, but decreases significantly with winds from the west or southwest, bringing air flowing from Chihuahuan Desert areas of West Texas or Northern Mexico.
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Winters in Austin are mild, although occasional short-lived bursts of cold weather known as "Blue Northers" can occur. January is the coolest month with an average daytime high of . The overnight low drops to or below freezing 12 times per year, and sinks below during 76 evenings per year, mostly between mid-December and mid-February. The average first and last dates for a freeze are December 1 and February 15, giving Austin an average growing season of 288 days, and the coldest temperature of the year is normally about under the 1991-2020 climate normals, putting Austin in USDA zone 9a.
Conversely, winter months also produce warm days on a regular basis. On average, 10 days in January reach or exceed and 1 day reaches ; during the 1991-2020 period, all Januarys had at least 1 day with a high of or more, and most (60%) had at least 1 day with a high of or more. The lowest ever recorded temperature in the city was on January 31, 1949. Roughly every two years Austin experiences an ice storm that freezes roads over and cripples travel in the city for 24 to 48 hours. When Austin received of ice on January 24, 2014, there were 278 vehicular collisions. Similarly, snowfall is rare in Austin. A snow event of on February 4, 2011, caused more than 300 car crashes. The most recent major snow event occurred February 14–15, 2021, when of snow fell at Austin's Camp Mabry, the largest two-day snowfall since records began being kept in 1948.
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Typical of Central Texas, severe weather in Austin is a threat that can strike during any season. However, it is most common during the spring. According to most classifications, Austin lies within the extreme southern periphery of Tornado Alley, although many sources place Austin outside of Tornado Alley altogether. Consequently, tornadoes strike Austin less frequently than areas farther to the north. However, severe weather and/or supercell thunderstorms can occur multiple times per year, bringing damaging winds, lightning, heavy rain, and occasional flash flooding to the city. The deadliest storm to ever strike city limits was the twin tornadoes storm of May 4, 1922, while the deadliest tornado outbreak to ever strike the metro area was the Central Texas tornado outbreak of May 27, 1997.
Natural disasters.
2011 drought.
From October 2010 through September 2011, both major reporting stations in Austin, Camp Mabry and Bergstrom Int'l, had the least rainfall of a water year on record, receiving less than a third of normal precipitation. This was a result of La Niña conditions in the eastern Pacific Ocean where water was significantly cooler than normal. David Brown, a regional official with the National Oceanic and Atmospheric Administration, explained that "these kinds of droughts will have effects that are even more extreme in the future, given a warming and drying regional climate." The drought, coupled with exceedingly high temperatures throughout the summer of 2011, caused many wildfires throughout Texas, including notably the Bastrop County Complex Fire in neighboring Bastrop, Texas.
2018 flooding and water crisis.
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In the fall of 2018, Austin and surrounding areas received heavy rainfall and flash flooding following Hurricane Sergio. The Lower Colorado River Authority opened four floodgates of the Mansfield Dam after Lake Travis was recorded at 146% full at . From October 22 to October 29, 2018, the City of Austin issued a mandatory citywide boil-water advisory after the Highland Lakes, home to the city's main water supply, became overwhelmed by unprecedented amounts of silt, dirt, and debris that had washed in from the Llano River. Austin Water, the city's water utility, has the capacity to process up to 300 million gallons of water per day; however, the elevated level of turbidity reduced output to only 105 million gallons per day. Since Austin residents consumed an average of 120 million gallons of water per day, the infrastructure was not able to keep up with demand.
2021 winter storm.
In February 2021, Winter Storm Uri dropped prolific amounts of snow across Texas and Oklahoma, including Austin. The Austin area received a total of of snowfall between February 14 and 15, with snow cover persisting until February 20.
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This marked the longest time the area had had more than of snow, with the previous longest time being three days in January 1985.
Lack of winterization in natural gas power plants, which supply a large amount of power to the Texas grid, and increased energy demand caused ERCOT and Austin Energy to enact rolling blackouts in order to avoid total grid collapse between February 15 and February 18. Initial rolling blackouts were to last for a maximum of 40 minutes, however lack of energy production caused many blackouts to last for much longer, at the peak of the blackouts an estimated 40% of Austin Energy homes were without power.
Starting on February 15, Austin Water received reports of pipe breaks, hourly water demand increased from 150 million gallons per day on February 15 to a peak hourly demand of 260 million gallons per day on February 16. On the morning of February 17 demand increased to 330 million gallons per day, the resulting drop of water pressure caused the Austin area to enter into a boil-water advisory which would last until water pressure was restored on February 23.
2023 winter storm.
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Beginning January 30, 2023 the City of Austin experienced a winter freeze which left 170,000 Austin Energy customers without electricity or heat for several days. The slow pace of repairs and lack of public information from City officials frustrated many residents. A week after the freeze and when Austin City Council members were proposing to evaluate his employment, City Manager Spencer Cronk finally apologized. On Thursday February 16, 2023, Cronk was fired by the Austin City Council for the city's response to the winter storm. Former City Manager Jesus Garcia was named Interim City Manager.
Parks.
The Austin Parks and Recreation Department received the Excellence in Aquatics award in 1999 and the Gold Medal Awards in 2004 from the National Recreation and Park Association.
To strengthen the region's parks system, which spans more than , The Austin Parks Foundation was established in 1992 to develop and improve parks in and around Austin. APF works to fill the city's park funding gap by leveraging volunteers, philanthropists, park advocates, and strategic collaborations to develop, maintain and enhance Austin's parks, trails and green spaces.
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Lady Bird Lake.
Lady Bird Lake (formerly Town Lake) is a river-like reservoir on the Colorado River. The lake is a popular recreational area for paddleboards, kayaks, canoes, dragon boats, and rowing shells. Austin's warm climate and the river's calm waters, nearly length and straight courses are especially popular with crew teams and clubs. Other recreational attractions along the shores of the lake include swimming in Deep Eddy Pool, the oldest swimming pool in Texas, and Red Bud Isle, a small island formed by the 1900 collapse of the McDonald Dam that serves as a recreation area with a dog park and access to the lake for canoeing and fishing. The Ann and Roy Butler Hike and Bike Trail forms a complete circuit around the lake. A local nonprofit, The Trail Foundation, is the Trail's private steward and has built amenities and infrastructure including trailheads, lakefront gathering areas, restrooms, exercise equipment, as well as doing Trailwide ecological restoration work on an ongoing basis. The Butler Trail loop was completed in 2014 with the public-private partnership 1-mile Boardwalk project.
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Along the shores of Lady Bird Lake is the Zilker Park, which contains large open lawns, sports fields, cross country courses, historical markers, concession stands, and picnic areas. Zilker Park is also home to numerous attractions, including the Zilker Botanical Garden, the Umlauf Sculpture Garden, Zilker Hillside Theater, the Austin Nature & Science Center, and the Zilker Zephyr, a gauge miniature railway carries passengers on a tour around the park. Auditorium Shores, an urban park along the lake, is home to the Palmer Auditorium, the Long Center for the Performing Arts, and an off-leash dog park on the water. Both Zilker Park and Auditorium Shores have a direct view of the Downtown skyline.
Barton Creek Greenbelt.
The Barton Creek Greenbelt is a public green belt managed by the City of Austin's Park and Recreation Department. The Greenbelt, which begins at Zilker Park and stretches South/Southwest to the Woods of Westlake subdivision, is characterized by large limestone cliffs, dense foliage, and shallow bodies of water. Popular activities include rock climbing, mountain biking, and hiking. Some well known naturally forming swimming holes along Austin's greenbelt include Twin Falls, Sculpture Falls, Gus Fruh Pool, and Campbell's Hole. During years of heavy rainfall, the water level of the creek rises high enough to allow swimming, cliff diving, kayaking, paddle boarding, and tubing.
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Swimming holes.
Austin is home to more than 50 public pools and swimming holes. These include Deep Eddy Pool, Texas' oldest human-made swimming pool, and Barton Springs Pool, the nation's largest natural swimming pool in an urban area. Barton Springs Pool is spring-fed while Deep Eddy is well-fed. Both range in temperature from about during the winter to about during the summer. Hippie Hollow Park, a county park situated along Lake Travis, is the only officially sanctioned clothing-optional public park in Texas. Hamilton Pool Preserve is a natural pool that was created when the dome of an underground river collapsed due to massive erosion thousands of years ago. The pool, located about west of Austin, is a popular summer swimming spot for visitors and residents. Hamilton Pool Preserve consists of of protected natural habitat featuring a jade green pool into which a waterfall flows.
Other parks.
In May 2021, voters in the City of Austin reinstated a public camping ban. That includes downtown green spaces as well as trails and greenbelts such as along Barton Creek.
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McKinney Falls State Park is a state park administered by the Texas Parks and Wildlife Department, located at the confluence of Onion Creek and Williamson Creek. The park includes several designated hiking trails and campsites with water and electric. The namesake features of the park are the scenic upper and lower falls along Onion Creek. The Emma Long Metropolitan Park is a municipal park along the shores of Lake Austin, originally constructed by the Civilian Conservation Corps. The Lady Bird Johnson Wildflower Center is a botanical garden and arboretum that features more than 800 species of native Texas plants in both garden and natural settings; the Wildflower Center is located southwest of Downtown in Circle C Ranch. Roy G. Guerrero Park is located along the Colorado River in East Riverside and contains miles of wooded trails, a sandy beach along the river, and a disc golf course.
Covert Park, located on the top of Mount Bonnell, is a popular tourist destination overlooking Lake Austin and the Colorado River. The mount provides a vista for viewing the city of Austin, Lake Austin, and the surrounding hills. It was designated a Recorded Texas Historic Landmark in 1969, bearing Marker number 6473, and was listed on the National Register of Historic Places in 2015.
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The Louis René Barrera Indiangrass Wildlife Sanctuary, located on the north shore of Lake Walter E. Long, is a park managed by the Austin Parks and Recreation Department with the goal of restoring the Blackland Prairie. While not open to the public, it is accessible through guided tours.
Demographics.
In 2020, there were 961,855 people, up from the 2000 United States census tabulation where there were people, households, and families residing in the city. In 2000, the population density was . There were dwelling units at an average density of . There were households, out of which 26.8% had children under the age of 18 living with them, 38.1% were married couples living together, 10.8% had a female householder with no husband present, and 46.7% were non-families. 32.8% of all households were made up of individuals, and 4.6% had someone living alone who was 65 years of age or older. The average household size was 2.40 and the average family size was 3.14.
In the city the population was spread out, with 22.5% of the population under the age of 18, 16.6% from 18 to 24, 37.1% from 25 to 44, 17.1% from 45 to 64, and 6.7% were 65 years of age or older. The median age was 30 years. For every 100 females, there were 105.8 males.
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The median income for a household in the city was , and the median income for a family was $. Males had a median income of $ compared to $ for females. The per capita income for the city was $. About 9.1% of families and 14.4% of the population were below the poverty line, including 16.5% of those under age 18 and 8.7% of those age 65 or over. The median house price was $ in 2009, and it has increased every year since 2004. The median value of a house which the owner occupies was $318,400 in 2019—higher than the average American home value of $240,500.
Race and ethnicity.
According to the 2010 United States census, the racial composition of Austin was 68.3% White (48.7% non-Hispanic whites), 35.1% Hispanic or Latino (29.1% Mexican, 0.5% Puerto Rican, 0.4% Cuban, 5.1% Other), 8.1% African American, 6.3% Asian (1.9% Indian, 1.5% Chinese, 1.0% Vietnamese, 0.7% Korean, 0.3% Filipino, 0.2% Japanese, 0.8% Other), 0.9% American Indian, 0.1% Native Hawaiian and Other Pacific Islander, and 3.4% two or more races.
According to the 2020 United States census, the racial composition of Austin was 72.6% White (48.3% non-Hispanic whites), 33.9% Hispanic or Latino, 7.8% African American, 7.6% Asian, 0.7% American Indian, 0.1% Native Hawaiian and other Pacific Islander, and 3.4% two or more races.
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A 2014 University of Texas study stated that Austin was the only U.S. city with a fast growth rate between 2000 and 2010 with a net loss in African Americans. , Austin's African American and non-Hispanic white percentage shares of the total population was declining despite the actual numbers of both ethnic groups increasing, as the rapid growth of the Latino or Hispanic and Asian populations has outpaced all other ethnic groups in the city. Austin's non-Hispanic white population first dropped below 50% in 2005.
Sexual orientation and gender identity.
According to a survey completed in 2014 by Gallup, it is estimated that 5.3% of residents in the Austin metropolitan area identify as lesbian, gay, bisexual, or transgender. The Austin metropolitan area had the third-highest rate in the nation.
Religion.
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Homelessness.
As of 2019, there were 2,255 individuals experiencing homelessness in Travis County. Of those, 1,169 were sheltered and 1,086 were unsheltered. In September 2019, the Austin City Council approved $62.7 million for programs aimed at homelessness, which includes housing displacement prevention, crisis mitigation, and affordable housing; the city council also earmarked $500,000 for crisis services and encampment cleanups.
In June 2019, following "Martin v. Boise", a federal court ruling on homelessness sleeping in public, the Austin City Council lifted a 25-year-old ban on camping, sitting, or lying down in public unless doing so causes an obstruction. The resolution also included the approval of a new housing-focused shelter in South Austin. In early October 2019, Texas Governor Greg Abbott sent a letter to Mayor Steve Adler threatening to deploy state resources to combat the camping ban repeal. On October 17, 2019, the City Council revised the camping ordinance, which imposed increased restrictions on sidewalk camping. In November 2019, the State of Texas opened a temporary homeless encampment on a former vehicle storage yard owned by the Texas Department of Transportation.
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In May 2021, the camping ban was reinstated after a ballot proposition was approved by 57% of voters. The ban introduces penalties for camping, sitting, or lying down on a public sidewalk or sleeping outdoors in or near Downtown Austin or the area around the University of Texas campus. The ordinance also prohibits solicitation at certain locations.
Economy.
The Greater Austin metropolitan statistical area had a gross domestic product (GDP) of $222 billion in 2022. Austin is considered to be a major center for high tech. Thousands of graduates each year from the engineering and computer science programs at the University of Texas at Austin provide a steady source of employees that help to fuel Austin's technology and defense industry sectors. As a result of the high concentration of high-tech companies in the region, Austin was strongly affected by the dot-com boom in the late 1990s and subsequent bust. Austin's largest employers include the Austin Independent School District, the City of Austin, Dell Technologies, the U.S. Federal Government, NXP Semiconductors, IBM, St. David's Healthcare Partnership, Seton Family of Hospitals, the State of Texas, the Texas State University, and the University of Texas at Austin.
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Other high-tech companies with operations in Austin include 3M, Apple (the largest campus outside of Cupertino), Amazon, AMD, Apartment Ratings, Applied Materials, Arm, Bigcommerce, BioWare, Blizzard Entertainment, Buffalo Technology, Cirrus Logic, Cisco Systems, Cloudflare, Crowdstrike, Dropbox, eBay, Electronic Arts, Flextronics, Facebook, Google, Hewlett-Packard, Hoover's, HomeAway, HostGator, Indeed, Intel Corporation, Meta, National Instruments, Nintendo, Nvidia, Oracle, PayPal, Polycom, Qualcomm, Rackspace, RetailMeNot, Rooster Teeth, Samsung Group, Silicon Labs, Spansion, TikTok, United Devices, VMware, X (formerly Twitter), Xerox, and Zoho Corporation. In 2010, Facebook accepted a grant to build a downtown office that could bring as many as 200 jobs to the city. The proliferation of technology companies has led to the region's nickname, "Silicon Hills", and spurred development that greatly expanded the city.
Tesla, Inc., an electric vehicle and clean energy company has its corporate headquarters in Austin inside Gigafactory Texas, a large vehicle assembly plant which employs over 20,000 people. The company expects to eventually have a staff of 60,000 in the Austin area as production ramps up.
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Austin is also emerging as a hub for pharmaceutical and biotechnology companies; the city is home to about 85 of them. In 2004, the city was ranked by the Milken Institute as the No. 12 biotech and life science center in the United States and in 2018, CBRE Group ranked Austin as #3 emerging life sciences cluster. Companies such as Hospira, Pharmaceutical Product Development, and ArthroCare Corporation are located there.
Whole Foods Market, an international grocery store chain specializing in fresh and packaged food products, was founded and is headquartered in Austin.
Other companies based in Austin include NXP Semiconductors, GoodPop, Temple-Inland, Sweet Leaf Tea Company, Keller Williams Realty, National Western Life, GSD&M, Dimensional Fund Advisors, Golfsmith, Forestar Group, EZCorp, Outdoor Voices, Tito's Vodka, Speak Social, and YETI.
In 2018, Austin metro-area companies saw a total of $1.33 billion invested. In 2018, Austin's venture capital investments accounted for more than 60 percent of Texas' total investments.
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Top employers.
According to Austin's comprehensive annual financial reports, the top employers by number of employees in the county are the following. "NR" indicates the employer was not ranked among the top ten employers that year.
Transportation.
In 2009, 72.7% of Austin (city) commuters drove alone, with other mode shares being: 10.4% carpool, 6% were remote workers, 5% use transit, 2.3% walk, and 1% bicycle. In 2016, the American Community Survey estimated modal shares for Austin (city) commuters of 73.5% for driving alone, 9.6% for carpooling, 3.6% for riding transit, 2% for walking, and 1.5% for cycling. The city of Austin has a lower than average percentage of households without a car. In 2015, 6.9 percent of Austin households lacked a car, and decreased slightly to 6 percent in 2016. The national average was 8.7 percent in 2016. Austin averaged 1.65 cars per household in 2016, compared to a national average of 1.8.
In mid-2019, TomTom ranked Austin as having the worst traffic congestion in Texas, as well as 19th nationally and 179th globally.
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Highways.
Central Austin lies between two major north–south freeways: I-35 to the east and the Mopac Expressway (Loop 1) to the west. US 183 runs from northwest to southeast, and SH 71 crosses the southern part of the city from east to west, completing a rough "box" around central and north-central Austin. Austin is the largest city in the United States to be served by only one Interstate Highway.
US 290 enters Austin from the east and merges into I-35. Its highway designation continues south on I-35 and then becomes part of SH 71, continuing to the west. Highway 290 splits from Highway 71 in southwest Austin, in an interchange known as "The Y." SH 71 continues to Brady, Texas, and Highway 290 continues west to intersect I-10 near Junction. Interstate 35 continues south through San Antonio to Laredo on the Mexican border. I-35 is the highway link to the Dallas-Fort Worth metroplex in Northern Texas. There are two links to Houston (US 290 and SH 71/I-10). US 183 leads northwest of Austin toward Lampasas.
In the mid-1980s, construction was completed on Loop 360, a scenic highway that curves through the hill country from near the 71/Mopac interchange in the south to near the US 183/Mopac interchange in the north. The iconic Pennybacker Bridge, also known as the "360 Bridge," crosses Lake Austin to connect the northern and southern portions of Loop 360.
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Tollways.
SH 130 is a bypass route designed to relieve traffic congestion, starting from Interstate 35 just north of Georgetown and running along a parallel route to the east, where it bypasses Round Rock, Austin, San Marcos and New Braunfels before ending at I-10 east of Seguin, where drivers could drive west to return to I-35 in San Antonio. The first segment was opened in November 2006, which was located east of Austin–Bergstrom International Airport at Austin's southeast corner on SH 71. Highway 130 runs concurrently with SH 45 from Pflugerville on the north until it reaches US 183 well south of Austin, at which point SR 45 continues west. The entire route of SH 130 is now complete. The final leg opened on November 1, 2012. The highway is noted for having a maximum speed limit of for the entire route. The section of the toll road between Mustang Ridge and Seguin has a posted speed limit of , the highest posted speed limit in the United States.
SH 45 runs east–west from just south of US 183 in Cedar Park to 130 inside Pflugerville (just east of Round Rock). A tolled extension of State Highway Loop 1 was also created. A new southeast leg of SH 45 has recently been completed, running from US 183 and the south end of Segment 5 of TX-130 south of Austin due west to I-35 at the FM 1327/Creedmoor Road exit between the south end of Austin and Buda. The 183A Toll Road opened in March 2007, providing a tolled alternative to US 183 through the cities of Leander and Cedar Park. Currently under construction is a change to East US 290 from US 183 to the town of Manor. Officially, the tollway will be dubbed Tollway 290 with "Manor Expressway" as nickname.
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